Enhancing User Comfort Models for Demand Response Solutions for
Domestic Water Heating Systems
Alexander Belov
1
, Alexandr Vasenev
2
, Paul J. M. Havinga
1
and Nirvana Meratnia
1
1
Pervasive Systems Research Group, University of Twente, Enschede, The Netherlands
2
Services, Cybersecurity and Safety Research Group, University of Twente, Enschede, The Netherlands
Keywords:
Demand Side Management, Comfort Modeling, Tank Water Heaters, User Interface.
Abstract:
Demand Side Management (DSM) solutions for domestic Water Heaters (WHs) can assist consumers benefit
financially by optimizing their energy usage. However, users’ dissatisfaction caused by negative impact of
DSM on their comfort may force them to reject the provided solutions. To facilitate DSM adoption in prac-
tice, there is a need to account for user comfort and to provide users with control strategies to balance energy
consumption and their comfort. Comfort models used for WHs typically account for only variability of the
temperature of running water. This paper extends such typical user comfort modeling approaches by consid-
ering the tap water flow as a possible variable during water activities. The model to relate tap flow and users’
comfort is the first contribution of this paper. The second contribution of this paper is the flow rate control
mechanism aligned with the user comfort model by means of the multi-objective optimization. Simulations
for different water activities demonstrate that the control mechanism coupled with the suggested user interface
can inform the user about multiple trade-offs between electric consumption and user flow discomfort, and thus
can inform about possibilities to rationally save energy for water heating. A set of suggestions on how to
organize the user interface is the third contribution of the paper.
1 INTRODUCTION
Demand Response (DR) as an integral part of De-
mand Side Management (DSM) can be identified as a
set of initiatives ”designed to induce lower electricity
use at times of high wholesale market prices or when
system reliability is jeopardized” (Commission et al.,
2006). DR is recognized by the European Commis-
sion as an important instrument to enhance energy ef-
ficiency and stability of the electrical grid (Directive,
2012).
Improving energy efficiency is impossible with-
out considering residential users involved in the de-
mand response. Final consumption in the residential
sector accounted for 26.65% of the total energy con-
sumption in the EU-27 in the year 2010 and continued
growing as reported by Eurostat (P. Bertoldi, 2012).
Therefore, reduction of energy consumption in the
residential sector can significantly contribute to de-
crease of the Union’s energy dependency and carbon-
dioxide emissions (Directive, 2010).
The adoption of DR programs balances in-
between how users perceive possible benefits and
shortcomings. By implementing DR, small resi-
dential consumers can gain numerous benefits such
as reduction of outages, more transparent and fre-
quent billing information, participation in the elec-
tricity market via aggregators, energy and financial
savings (Giordano et al., 2011). Notwithstanding,
there is still a significant level of consumer resistance
to participating in DR projects, mainly because con-
sumers are afraid of losing control of devices in their
own household and are sceptical about new electric-
ity rates, (Magazine, 2014). Consumers’ concerns
and uncertainties create a barrier for the wide-scale
uptake of DR solutions, which in turn decreases the
overall profitability of DR measures (Sharon Mecum,
2002).
The need for involving consumers in sustainable
consumption has been highlighted by the EC Task
Force for Smart Grids ”the engagement and educa-
tion of the consumer is a key task in the process as
there will be fundamental changes to the energy retail
market” (Force, 2010). The European Communica-
tion on smart grids underlines the importance of con-
sumer awareness by stating that ”developing smart
grids in a competitive retail market should encour-
age consumers to change behaviour, become more
Belov, A., Vasenev, A., Havinga, P. and Meratnia, N.
Enhancing User Comfort Models for Demand Response Solutions for Domestic Water Heating Systems.
In Proceedings of the 5th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 2016), pages 201-212
ISBN: 978-989-758-184-7
Copyright
c
2016 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
201
active and adapt to new smart’ energy consumption
patterns” (Commission, 2011).
Consumers can modify their energy consumption
habits based on direct feedback about their energy us-
age (Directive, 2009).
To be useful, information about energy consump-
tion and estimates for energy costs should be pro-
vided in a timely manner and in an easily understand-
able format (Directive, 2012). Typically, the task
of informing users is handled by means of various
user interfaces (UIs) integrated into automated home
demand response solutions for, among others, room
heating, air-conditioning, water heating systems, and
other electric loads (Lu and Zhang, 2013; Giorgio and
Pimpinella, 2012; Koutitas, 2012). Several off-the-
shelf UI solutions are available in the market today
(Nest, 2015; Honeywell, 2015).
A number of projects are now focusing on con-
sumer engagement in DR (Jorgensen et al., 2011;
to Grid Project, 2012; Project, 2011; Sæle and
Grande, 2011). For example in the EcoGrid
EU project, consumers having demand response-
equipped devices and intelligent controllers can react
to real-time price signals (Jorgensen et al., 2011).
The Ewz-Studie Smart Metering project aims to
assess consumer response to different DRs through
use of tools such as in-home displays, expert ad-
vice, social competition and social comparison. Other
projects like Consumer to Grid project intend to
measure the behavioral change induced by various
feedback mechanisms such as monthly bills, web-
site, smart phone APPs and ad-hoc feedback gadget
(to Grid Project, 2012).
Despite of all these tools, ready-to-deploy prod-
ucts, and projects, the expressed European view on
energy saving schemes indicates the need for further
in-depth consideration of ways for improving energy
utilization in individual households. Essentially, this
concerns both questions about how to improve the ef-
ficiency of energy usage and how to communicate the
related information with the consumer.
1.1 Modeling User Comfort for
Domestic Water Heaters
This paper concentrates on the specific problem of
”how to improve the efficiency of energy consump-
tion of a domestic electric storage-tank water heater
load (WH) with respect to user comfort and how to
enhance consumers’ awareness about their electricity
expenses for water heating?”. The case of domestic
water heaters is particularly relevant to the residen-
tial energy consumption because they make up more
than two thirds of the total household consumption
together with room heaters and air conditioners in
European countries (Comission, 2011). Furthermore,
since tank water heating units are still present in a pre-
vailing number of European households and because
of their capability to store thermal energy, they serve
as a good example of a household loads.
Previously, a number of approaches (e.g. (Belov
et al., 2015a; Sepulveda et al., 2010; Du and Lu,
2011; Pedrasa et al., 2009; Dlamini and Cromieres,
2012)) have been suggested to account for user com-
fort with respect to WHs in order to minimize com-
fort disruptions and hence to increase attractivness
of these DR solutions to the customers. Majority of
these works deal with the thermal discomfort caused
by uncomfortable tap water temperature. They as-
sume that the tap flow rate is xed during the entire
water usage and pre-determined by the user.
However, additional savings can be achieved by
investigating opportunities to reduce the tap flow rate.
For instance, modern water efficient faucets can save
water during tasks performedin running water by lim-
iting the flow rate (Agency, 2015) or by interrupt-
ing the water flow when it is not needed (Digital,
2015; Stepon, 2015), which in turn reduces the wa-
ter heater’s demand and leads to energy savings.
This paper argues that relaxing the assumption
about the fixed tap flow can open up opportunities
for additional electricity savings. A loosely-defined
flow rate, suggested by the user and related to the
user comfort model, can be a subject of sophisti-
cated control. Additionally, by carefully examining
the amount of tap hot water withdrawn, the inten-
tions to save energy and water usage can be united.
As these objectives are highly relevant for the green
energy paradigm, this approach can support smoother
transition towards green energy solutions.
In our view, three aspects should be considered to
enable efficient utilization of both water and energy
for water heating. Firstly, a model should be devel-
oped to accurately account for relations between tap
water flow rate and user comfort. Secondly, a mech-
anism to control the WH with regard for this model
should be developed. Finally, information about the
control possibilities and their impact on energy con-
sumption for water heating and user satisfaction with
the tap flow rate should be represented to a user by
means of a clear and understandable user interface.
Together, these topics highlight multiple intricate in-
terrelations between energy and water savings, user
comfort, and possibilities for user control of flow-
adjustable water events.
We build on our previous research that concerns
user comfort described in (Belov et al., 2014; Belov
et al., 2015a; Belov et al., 2015b). Previously, we sug-
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202
gested a system built around the water activity (WA)
concept where a WA of a specific duration executed
by a user has two parameters, i.e. the tap water tem-
perature and water flow (Belov et al., 2015b). In this
paper we extend the user comfort model, that has pre-
viously accounted only for a user satisfaction with
water temperature (Belov et al., 2015a), and introduce
a new flow-based discomfort metric. This paper also
suggests the way to organize an interface to visual-
ize interrelations between energy, flow rate, and user
comfort to the end-user.
Therefore, this paper presents three main contri-
butions (1) a model that can link energy savings and
water usage and show their effect on one another, (2)
a system incorporating this model together with the
flow-rate control mechanism is proposed, and (3) a
way of how the system can interact with the user.
The rest of the paper is organized as follows. Sec-
tion 2 represents modeling of the water heater system,
describes the scenario of hot water usage and the flow
rate control. The existing approach for user flow dis-
comfort modeling is discussed in Section 2.3 and up-
dated later on in the paper. Initial considerations for
the user interface are outlined in Section 2.5. In Sec-
tion 3 we apply a multi-objective optimization to un-
fold an explicit relation between electricity expenses
for water heating and user flow discomfort. A role of
the user interface and suggestions to its implementa-
tion are also presented in Section 3. Section 4 exhibits
and discusses the simulation results for the selected
water activities. Some directions for the future work
are outlined in Section 5 and our conclusions are sum-
marized in Section 6.
2 MODELING HOT WATER
SUPPLY
This section introduces importantconcepts for model-
ing water heater operation and user discomfort. These
concepts will be used in subsequent sections of the
paper.
2.1 Water Heater Operation
In this paper we consider an electric storage-tank wa-
ter heater (WHs) used to heat tap water in a house-
hold. Most of such WHs operate in a cyclic man-
ner. This means that the heating elements of a WH
are continuously turned on and off to maintain the
temperature inside the tank within some temperature
deadband. More specifically, the WH remains on, if
its internal temperature is below the upper setpoint
temperature. When the upper setpoint is reached, the
heating elements are shut down till the temperature
in the tank drops below the lower setpoint. There
is extensive literature available on modeling of WHs,
see for instance (Kondoh et al., 2011; Dolan et al.,
1996; Lane and Beute, 1996). In contrast, in this pa-
per we consider a small-sized domestic WH assuming
that entire water in the tank is at the same tempera-
ture, i.e. non-stratified. In this regard, we adopt the
following thermodynamic model of the well-mixed
WH described in (DOE, 2013):
MC
dT
dt
= P
e
+ P
cw
P
hw
P
loss
(1)
where M is the water mass in the tank, C is specific
temperature of water, P
e
is the thermal power supplied
by the heating elements, P
cw
and P
hw
are cold water
inflow and hot water outflow of the tank, and P
loss
is
the heat losses to the ambient.
Normally, the preferred tap water temperature and
flow rate is set by using the tap mixer. The mentioned
components of the model are interrelated as indicated
in Figure 1.
Figure 1: Considered Setup.
Energy and mass balance in the mixing device can
be expressed as:
(
P
d
= P
hw
+ P
cw2
˙m
d
= ˙m+ ˙m
cw
(2)
where P
d
is the tap water thermal power demanded by
the user, P
hw
is the power flow from the tank, P
cw2
is
cold water from the main controller, and ˙m
d
, ˙m, ˙m
cw
are the demanded, hot and cold water mass flow rates,
respectively.
The mixer merges hot and cold water flows in
a certain proportion which basically determines how
fast the temperature in the tank T(t) will fall during
the water activity (WA). (2) expresses that the ratio
between the hot water and cold water flow rates in the
mixer bind together the temperature inside the tank
T(t), the demanded temperature T
d
(t), and the cold
water temperature T
cw
at every moment of time:
k =
˙m
˙m
cw
=
T
d
(t) T
cw
T(t) T
d
(t)
(3)
Enhancing User Comfort Models for Demand Response Solutions for Domestic Water Heating Systems
203
Time, [min]
0 1 2 3 4 5 6 7
Temperature, [C]
15
20
25
30
35
40
45
50
55
60
65
70
0 1 2 3 4 5 6 7
Electric Consumption, [kWh]
0
0.1
0.2
0.3
0.4
Tank Temperature
Tap Water Temperature
Electric Consumption
Lower Setpoint Temperature
Figure 2: WH during 10-minute WA.
2.2 Hot Water Usage & Flow Control
The main focus of this paper is on improvement of
energy utilization in a domestic WH by means of the
WH control mechanism that treats the tap flow rate as
a controllable parameter.
As it can be seen from (1), hot water demand to-
gether with heat losses to the environment contribute
to the drop of thermal energy inside the water stor-
age. Noteworthy is that heat losses to the ambient are
neglectfully small compared with the heat discharge
due to the hot water usage (Du and Lu, 2011). One
can conclude from (1) and (2) that any outflow from
the tap ˙m
d
> (P
e
P
loss
)/[C(T
d
T
cw
)] leads to the de-
crease of temperature inside the WH as shown in Fig.
2. As a result, the actual tap water temperature T
d
will
also decline over time, which can bring the user some
thermal discomfort.
Unlike the above typical scenario for the flow-
fixed hot water usage, this paper explores the flow-
adjustable scenario where the user desires the fixed
tap water temperature for a WA. The user request for
the fixed temperature can be fulfilled by controlling
the proportion of hot and cold water flows in the mix-
ing device represented by (3). The analysis of this
equation done in our previous studies (Belov et al.,
2014) highlights the possibility to maintain the user
request for the fixed temperature by progressively in-
creasing the hot water flow from the tank, while grad-
ually lowering the cold water inflow in the mixer
throughout the WA.
A hot water management system can handle water
flow in the tap mixer in a stepwise manner as illus-
trated in Fig. 3. The figure shows a case when a user
is willing to obtain tap water at 45
C. However, the
tap water temperature naturally goes down because
(i) the cold water enters the tank and (ii) the power of
electric heating elements cannot typically recover the
tank temperature during the water usage. Thus, the
flow controller adjusts hot and cold water flows every
minute to maintain the tap water temperature at the
desired level.
0 1 2 3 4 5 6 7
40
45
50
55
60
t, [min]
T, [C]
Tank Temperature
Tap Water Temperature
0 1 2 3 4 5 6 7
0
2
4
6
8
10
t, [min]
Water Flow Rate, [L/min]
Outflow from tank
Cold water flow
Tap flow
Desired Temperature
Figure 3: Flow Management in Mixing Controller.
2.3 Tap Flow Rate Discomfort
The concepts of the flow-adjustable hot water con-
sumption and the flow control associated with it and
presented in Section 2 call for a careful consideration
of impacts of the flow control on user comfort.
The conceptof the flow rate discomfort introduced
previously in (Belov et al., 2014) can be illustrated
by the following example. Let us consider a person
who want to take a 7-minute shower at the fixed wa-
ter temperature of 45
C. Such water service can be at-
tained by means of the flow controller that maintains
the wanted temperature by regulating the hot and cold
water flows in a step-wise manner as discussedin Sec-
tion 2.2. More precisely, there can be multiple solu-
tions to this control problem, each of which resulting
in a different water flow from the shower head. Two
of these solutions are shown in Fig. 4(a).
As it can be seen from Fig. 4(a), both control so-
lutions lead to the tap water flows uncomfortable for
the user. In fact, the user can experience distinct dis-
satisfaction at every step of control which is caused
by the mismatch between the currently provided flow
and the flow rate desired by the user (10 [L/min]). To
quantify the user inconvenience of having unsatisfac-
tory flow rate for the entire WA, we take instantaneous
flow deflections over time as illustrated in Fig. 4(b).
We suppose that the time during which the user expe-
riences the undesirable flow is significant for the WA
accomplishment. This means that if the duration of
discomfort is short enough, the user might still pro-
ceed with the WA. Otherwise the user might refuse to
continue. Moreover, flow variation considered over
time can indicate the amount of overused/undelivered
liters of water. This can be crucial in some scenarios,
for example, in filling a bath. To this end, we accumu-
late all instantaneous deviations of the supplied water
flow over the entire duration of a WA. The total flow
rate discomfort can be then described by:
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204
0 1 2 3 4 5 6 7
0
2
4
6
8
10
t, [min]
Water Flow Rate, [L/min]
Outflow from tank
Cold water flow
Tap flow
Desired Flow Rate
Solution #2
Solution #1
(a)
(b)
Figure 4: Flow Rate Discomfort.
A
˙m
d
=
N
i=1
| ˙m
exp, i
˙m
d, i
|t, (4)
where N is the number of control steps, ˙m
exp, i
is the
desired flow rate at i-th step, ˙m
d, i
is the tap water flow
provided at step i, and t is the size of the control
step.
2.4 Effect on Thermal Discomfort
Apart from the flow rate discomfort, the user can also
experience a drop of tap water temperature within ev-
ery step of the flow control as illustrated for a single
step in Fig. 5. Noticeably, different people typically
have different tolerance to cold and hot water due to
individual skin sensitivity (Robertson et al., 2006). To
estimate the levels of thermal discomfort the user can
experience during the flow control, we employ the
thermal discomfort model presented earlier in (Belov
et al., 2015a). The model takes into account that dif-
ferent people can tolerate the tap water temperature
deflections differently by incorporating personal tem-
perature discontent functions.
2.5 Hot Water Management System
(HWMS) and User Interface
In addition to the flow rate control mechanism that
concerns user comfort, this paper also presents a
Figure 5: Motivation Example to Consider Thermal Dis-
comfort During Flow Control.
Figure 6: System’s Functionality (no arrows show bi-
directional links).
novelapproach for developinga clear and understand-
able user interface (UI). The suggested UI is part of
a bigger hot water management system (HWMS) that
consists of a smart tap and main controller for the WH
(Belov et al., 2015b). The diagram that gives a gen-
eral idea on how a user can interact with the system
and its major components are shown in Fig. 6.
Figure 6 illustrates that the main controller in-
cludes GUI, database controller Ctrlr. DB’ that stores
all user preferences and optimization results, predic-
tion module that builds a daily timetable of the ex-
pected WAs and the Scheduler that calculates the out-
comes of the flow control and executes it. The user
can communicate with the HWMS through GUI that
can be realized on diverseuser gadgets and digital dis-
play. GUI serves three main purposes (a) to collect
the needed for the Scheduler comfort related infor-
mation from the user, (b) to represent control options
found by the Scheduler, and (c) to obtain user feed-
back about the offered options. Once the user has es-
timated and chosen the desired control outcome, the
steering signals from the Scheduler are fed to the set-
point control manager to change the thermostat cur-
rent setpoint temperature setting and start/stop heat-
Enhancing User Comfort Models for Demand Response Solutions for Domestic Water Heating Systems
205
ing as well as to the Smart Tap to adjust the flow ratio
specified in (3).
All in all, at every step of the flow control, the
system withdraws a small portion of hot water from
the tank and mixes it with cold water to achieve
the wanted tap water temperature. Obviously the
stronger is the hot flow rate at every step, the (po-
tentially) higher is the tap water temperature. How-
ever, a strong step-increase of the hot flow can lead
to a rapid WH discharge and thereby to the thermal
discomfort. The flow control seeks optimal combi-
nations of {T
i
, ˙m
i
, ˙m
cw,i
},i N, where T
i
is the tank
temperature at the beginning of step i and N is the to-
tal number of control steps. Consequently, (4) also
implies an implicit link between the flow rate discom-
fort and electric consumption for preheating. Having
such relationship in explicit form before the WA the
user can estimate the consequences of current com-
fort settings on energy consumption with respect to
the heat currently available in the tank.
3 LINKING ENERGY
CONSUMPTION TO FLOW
RATE DISCOMFORT
Since the flow control outlined in Section 2.2 should
be executed with respect to the user acceptable level
of the flow rate discomfort as discussed in Section 2.3,
the flow control algorithm should be coupled with the
user flow comfort model. In order to explicitly incor-
porate the comfort model into the flow control scheme
the relationship between the user flow discomfort and
electricity expenses should be found.
3.1 Pre-heating Procedure
To maintain the tap water temperature at the requested
level and to ensure the accepted level of the flow rate
discomfort, there might be a need to pre-store addi-
tional heat in the WH, taking into account the con-
straint for the maximum tank water temperature dic-
tated by safety reasons (InterNACHI, 2015). If the
SoC of the WH at the beginning of water usage is
insufficient to suit the user comfort choice, the main
controller of the system initiates a pre-heating proce-
dure.
The HWMS reminds the user about the expected
WA by sending him a notification message. The mes-
sage contains different options to provide the hot wa-
ter service to the user. Once the user has acknowl-
edged one of the offered alternatives, the system esti-
mates the required SoC at the start-up of the WA and
Time, [min]
06:30 06:45 07:00 07:15 07:30 07:45 08:00 08:15
Temperature, [C]
20
25
30
35
40
45
50
55
60
65
70
75
80
85
0
0.4
0.8
1.2
1.6
2
2.4
2.8
3.2
3.6
4
Tank Temperature
Electric Consumption
WA
Pre-heating Period
User Notification
Figure 7: Pre-heating Procedure (dashed lines - WH regular
operation, solid lines - WH pre-heating).
finds the optimal time to start the pre-heating proce-
dure. The user might end up with a higher energy
consumptionthan usual, if the requested comfort level
was high as demonstrated in Fig. 7. Here we make an
assumption that no other WAs can occur in the in-
terval in which the user approves one of the offered
solutions and the WA starts.
3.2 Multi-objective Optimization &
Pareto Front
In order to explicitly link the electric consumption
for water pre-heating with the user flow rate dis-
comfort, we apply a multi-objective optimization ap-
proach. We consider minimizing energy consumption
and minimizing flow rate discomfort as two conflict-
ing objectives. In general, multi-objective optimiza-
tion allows to manage multiple goals to be achieved
simultaneously subject to a set of constraints. If
achievement of one goal has a negative impact on at-
taining another goal, two goals are said to be conflict-
ing. From mathematical point of view, minimization
(or maximization) of conflicting objective functions
leads to a number of optimal solutions that make up
Pareto front (Caramia and Dell’Olmo, 2008). Pareto
front is characterized in the way that switching from
one solution to another on the front improves one of
the conflicting objectives and degrades the value of
another. The approach to align two goals by means
of the multi-objective optimization and the resulting
flow control mechanism is the first contribution of this
paper.
3.3 Objective Function I - Minimum
Energy Consumption
To formulate the first objective function, we assume
that the water heater can be initially at any allowed
temperature depending on the previous history of wa-
ter usage. By solving the differential equation (1)
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206
electric consumption for pre-heating E
e
in the period
t
pre
can be expressed as:
E
e
(t
pre
) = P
e
t
pre
=
αP
e
log[β f(SoC(0),SoC(t
pre
))]
(5)
, where α and β are coefficients dependent on engi-
neering parameters of the WH; SoC(0) and SoC(t
pre
)
are the SoC of the WH in the beginning and at the end
of the preheating period respectively.
Aiming at minimum electric energy consumption,
we set the objective F
1
= min[E
e
(t
pre
)] as the first ob-
jective function for our multi-objective optimization.
3.4 Objective Function II - Maximum
User Flow Rate Comfort
To account for variations in user perceptions of the
water flow, we extend the discomfort metric A
˙m
d
(t)
represented earlier in Section 2.3 by incorporating the
individual discontent function F
˙m
d
. The discontent
function F
˙m
d
reflects how deviations of the tap water
flow are important to a person in a specific scenario
of water usage. Thus this extension adds flexibility to
the original comfort model and enables to differenti-
ate between discomfort levels of multiple users. We
assume that the individual discontent function estab-
lishes a linear relationship between user dissatisfac-
tion and tap water flow deflections at any time step
i:
F
˙m
d
,i
=
0 , if ˙m
d, i
˙m
d, comf
;
α
1
˙m
d, i
+ β
1
, if ˙m
d, i
tol
;
α
2
˙m
d, i
+ β
2
, if ˙m
d, i
+
tol
;
1 , otherwise;
(6)
where ˙m
d, i
is the tap water flow rate at step i;
˙m
d, comf
is the range of flows comfortable for the
user; α
1
< 0,α
2
> 0,β
1
,β
2
are some coefficients;
tol
and
+
tol
are lower and upper flow tolerance zones as
illustrated in Fig. 8:
Figure 8: Discontent Function.
Then the updated user flow rate discomfort model
can be formalized as:
D
˙m
d
=
N
i=1
F
˙m
d
,i
A
˙m
d
,i
(7)
where F
˙m
d
,i
is the user discontent level reached at step
i; A
˙m
d
,i
specifies the area resulted from the flow ˙m
d, i
deviation from the comfort zone ˙m
d, comf
during step
i.
The second objective function can be formalized
as F
2
= min[D
˙m
d
].
The designed user flow rate comfort model is the
second contribution of this paper.
3.5 User Interface
The necessity of attaining Pareto fronts in our case is
mainly dictated by two reasons: (a) its convenience
of representing an extensive information about multi-
objective optimization results in a compact form that
is abstract enough to hide unnecessary details from
the user; (b) its capability to plainly illustrate a wide
range (possibly infinite) of alternative solutions that
the user can accept while pursuing either of the above
goals. This means that the user can observe not only a
single solution that satisfies his current choice but also
a variety of other options that might also influence
his actual decision. All in all, it can be assumed that
the user supported with multiple trade-offs can make
more conscious and justified choices when balancing
energy consumption/costs and personal comfort.
In principal, the system starts operating with
checking the available comfort models for the planned
activities. If the system starts up freshly or if some of
the user comfort parameters from the previous runs
are missing, the Scheduler requests ’Ctrlr. DB’ to de-
rive the needed inputs from the user via GUI as shown
in Fig. 9. The needed input parameters consist of (a)
user comfort preferences for the planned WAs, and
(b) updated WAs schedules. The former inputs can be
entered in the form of user comfort model parameters,
though some of them can be automatically set within
the system calibration phase.
As it can be concluded from Fig. 9, the important
role of the GUI is to check the user feedback about the
quality of hot water service provided. The user feed-
back feature of the GUI is essential for correct provi-
sion of hot service with respect to the user’s comfort
choice and the amount of money (s)he is ready to pay
for it. In calibration phase, the GUI can initiate a test
program that tends to automatically tune the tap flow
rate during the selected WAs, check the user response,
and re-adjust some of the comfort model parameters.
The HWMS and the flow rate control mechanism
that it implements delegate to the user the responsi-
Enhancing User Comfort Models for Demand Response Solutions for Domestic Water Heating Systems
207
Figure 9: System Calibration.
bility for making a decision concerning how realis-
tic and comfortable is the current user flow comfort
model and how much money to pay. Therefore, at this
stage the system is fully user-centric and governed by
the user’s choice. It does not take decisions about
how much comfort to provide and at what expense
instead of the user, but it rather works out control ac-
tions based on the information from the user and of-
fers different control alternatives to the user, assisting
him in making a rational comfort-energy choice.
4 PERFORMANCE EVALUATION
AND VALIDATION
In the system calibration phase the controller utilizes
available user comfort model to provide the user with
the feedback about the upcoming WA by calling the
Pareto Front Calculation Block (PFCB) as shown in
Fig. 9. In PFCB the Scheduler component of the sys-
tem solves the the multi-objective optimization prob-
lem, simultaneously resolving the objectives F
1
and
F
2
.
We present how the PFCPB retrieves solutions
(Pareto front) for several WAs regularly performed at
home to demonstrate the existing connection and to
find an explicit relationship between the above two
goals. The chosen WAs are listed together with their
estimated flow rates and volume values (Wid´en et al.,
2009; Kaye, 2009; EngineeringToolbox, ) in Table 1.
We first build Pareto fronts for the selected WAs
with varied duration aiming to estimate the maximum
and minimum values of the shifted electric consump-
Table 1: WAs Selected For Simulations.
WA
Volume,
Estimated
Flow
Rate,
Flow
Range,
[L]
[L/min] [L/min]
Wash Hands
a
0.7 ... 7.5 6 2 ... 9
Dishwashing
b
38 ...75 9 6 ...25
Shower
c
32 ...225 15 8 .. . 25
a
Bath tap, running water.
b
Kitchen tap, running water.
c
Mains fed.
Note: There is little statistical data on hot water usage per activity available. Some
of the missing data per activity is replaced by data per water source location.
Table 2: Simulations of WAs with Different Duration.
Duration,
[min]
Comf.
Flow
Range,
[L/min,
L/min]
Flow
Tolerance,
[L/min,
L/min]
Temp.
Tolerance,
[
C,
C]
0.5
[10,12] [40,45]
7 [8,12]
15
Figure 10: WAs & Parameters Used for Simulations.
tion and the resulting flow rate discomfort. The values
used in these simulations are listed in Table 2.
We further carry out simulations for 7-minute
WAs in distinct ranges of tap water temperatures and
flow rates desired by the user while setting the fixed
lower boundaries for the flow tolerance zones
tol
and
+
tol
as well as the thermal tolerance zones T
tol
as
shown in Fig. 10.
Since the flow rate discomfort D
˙m
d
depends on
the size of the control step (via term A
˙m
d
,i
in (7), we
also estimate the effect of altering the step size on
E
e
(t
pre
) and D
˙m
d
. In addition, we show how D
˙m
d
affects the thermal discomfort D
T
following the dis-
cussion in Section 2.4.
4.1 Simulation Results
Pareto optimal solutions for WAs with different du-
ration can be found in Fig. 11. The graphs repre-
sent the electric energy consumed for water preheat-
ing E
e
(t
pre
) as a function from the flow rate discom-
fort D
˙m
d
. The discomfort is shown in percentage as a
share of the maximum D
˙m
d
for the current parameters
of water usage. The color of each solution on Pareto
SMARTGREENS 2016 - 5th International Conference on Smart Cities and Green ICT Systems
208
(a)
(b)
Figure 11: Varied Duration ((a) 7-minute WA, (b) 15-
minute WA).
front refers to the certain range of tap water flows
and the time during which the user experiences D
˙m
d
.
The bar exhibits these values in the following format
[ ˙m
d, min
, ˙m
d, max
],t
D
, which is the minimum and the
maximum flows reached during the WA and the dura-
tion of D
˙m
d
. The two sequential solutions from Fig.
11(b) that have different D
˙m
d
and equal E
e
(t
pre
) are
plotted in Fig. 12.
The influence of the control step size on the flow
discomfort D
˙m
d
is demonstrated in Fig. 13. The ther-
mal discomfort D
T
has been calculated for every solu-
tion on Pareto front of the considered WAs. The con-
nection between two different types of discomfort, D
T
and D
˙m
d
, is represented for the 7-minute WA in Fig.
14(a). Colorful curve illustrates a number of Pareto
optimal solutions where each color refers to a certain
tap water temperature range [T
max
,T
min
] and discom-
fort duration T
DISC
specified in the bar. We also show
how the relation between D
T
and D
˙m
d
depends on the
control step size in Fig. 14.
4.2 Discussion of Results
According to the set of Pareto optimal solutions
shown in Fig. 11, the user can reduce D
˙m
d
at the cost
of the increased E
e
(t
pre
) and vice versa, indicating
that a non-linear negative correlation between these
functions.
It is noteworthy that in case of intensive water us-
age the flow controller cannot handle the user request
for the fixed temperature during the entire WA. For
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
30
35
40
45
50
55
60
65
70
75
80
85
90
95
t, [min]
T, [C]
Tank Temperature
Tap Water Temperature
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
2
4
6
8
10
12
14
t, [min]
Water Flow Rate, [L/min]
Outflow from tank Cold water flow Tap flow
Tolerance Boundary
Lower Comfort Boundary
Upper Comfort Boundary
Desired Temperature
(a)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
2
4
6
8
10
12
14
t, [min]
Water Flow Rate, [L/min]
Outflow from tank Cold water flow Tap flow
Tolerance Boundary
Upper Comfort Boundary
Lower Comfort Boundary
(b)
Figure 12: 15-minute WA & Fully Charged Tank ((a) D
˙m
d
=
10%, (b) D
˙m
d
= 3%.
example, the tap water temperature inevitably drops
within the last 2 minutes of the 15-minute WA as rep-
resented in Fig. 12(a). It can be explained by the
limited capacity of the tank. Although the WH is pre-
heated to the maximum temperature defined by safety
reasons (90
C in our case), the thermal energy accu-
mulated in the tank is insufficient to provide the user
with tap water of the preferred 45
C along the whole
WA.
As it can be seen from Fig. 11(b) minimization
of D
˙m
d
for long lasting WAs can be achieved with-
out maximizing electric consumption. This situation
takes place because the WH is fully charged and can-
not be further heated. More rigorous examining of
the neighbor solutions on Pareto front points out that
such decrease of D
˙m
d
results in a steep jump of the
resulting tap water flow rate ˙m
d
as depicted in Fig.
12. Such sudden acceleration of the water flow can
bring extra inconvenience to the user and thus should
be also taken into account during the flow control.
As it follows from the simulation results illus-
trated in Fig. 13, long time lags between the flow
control actions allow to minimize D
˙m
d
spending less
electricity than in the case of the frequent flow regu-
lation. While the extension of control steps has a pos-
itive effect on D
˙m
d
and E
e
(t
pre
), it has an negative
effect on the thermal discomfort D
T
as shown in Fig.
14. The longer steps permit the water in the tank cool
down to the lower temperature which results in the in-
crease of D
T
. Considering the contrary effects of the
step size on the two types of discomfort and E
e
(t
pre
)
a compromise between D
˙m
d
and D
T
can be achieved
by incorporating D
T
as the third objectivefunction for
Enhancing User Comfort Models for Demand Response Solutions for Domestic Water Heating Systems
209
0 10 20 30 40 50 60 70 80 90 100
2
3
4
5
6
Flow Rate Discomfort, [%]
Energy, [kWh]
Time Step Size =5 sec
Time Step Size =60 sec
Time Step Size =140 sec
Time Step Size =210 sec
(a)
0 20 40 60 80 100
3
4
5
6
7
8
Flow Rate Discomfort, [%]
Energy, [kWh]
Time Step Size =5 sec
Time Step Size =30 sec
Time Step Size =60 sec
Time Step Size =300 sec
(b)
Figure 13: Varied Size of Timesteps ((a) 7-minute WA, (b)
15-minute WA).
the multi-objective optimization problem and finding
the optimal timing for the flow control actions.
The obtained Pareto fronts in Fig. 11 represent a
simple, yet efficient way to visualize the detailed in-
formation about multiple solutions for flow rate con-
trol and their effect on energy consumption and user
comfort. By picking any of the suggested solutions on
Pareto front via the GUI the user can further demand
the information of any level of complexity about the
expected water usage such as the resulting tap and
tank water temperature values, water flow rates in the
whole hot water supply system and duration of D
˙m
d
at every moment of the expected WA, for example, as
shown in Fig. 11(a) and Fig. 12.
5 FUTURE WORK
The normal operation of the WH implies that the hot
water outflow from the tank induces the equal inflow
of cold water, which creates the needed pressure to
deliver hot water to the tap and causes the insider WH
0 20 40 60 80 100
0
20
40
60
80
100
Flow Rate Discomfort, [%]
Thermal Discomfort, [%]
Time Step Size =5 sec
Time Step Size =60 sec
Time Step Size =140 sec
Time Step Size =210 sec
(a)
Flow Rate Discomfort, [%]
0 20 40 60 80 100
Thermal Discomfort, [%]
0
20
40
60
80
100
Time Step Size =5 sec
Time Step Size =30 sec
Time Step Size =60 sec
Time Step Size =300 sec
(b)
Figure 14: Effect on Thermal Discomfort ((a) 7-minute WA,
(b) 15-minute WA).
temperature to drop. One might think of the ways to
cut the cold water inflow in the WH so that the insider
temperature remains fixed during WAs and there is
sufficient pressure in the hot water pipe.
In our studies we applied a linear relationship to
model the user dissatisfaction with the aberrant tap
water flow. The future work can concentrate on ob-
taining the realistic shapes of individual discontent
functions.
Some extra work on UI improvement and real-
world testing can be also suggested. Comparative
feedback through the UI may lead to a sense of com-
petition, whereas social comparison and social pres-
SMARTGREENS 2016 - 5th International Conference on Smart Cities and Green ICT Systems
210
sure may be especially effective when relevant oth-
ers are used as a reference group (Abrahamse et al.,
2005; Team, 2011). On the other hand, it is essen-
tial to provide a feedback about individual’s influence
on aggregated energy consumption (e.g., neighbor-
hood), because having an insight about personal con-
tribution to a global energy use/CO2 reduction prob-
lem a householder can estimate his input as valuable
and continue to actively save energy (Abrahamse and
Steg, 2011). Applying these phsycological principles
to electric energy conservation domain means that the
HWMS should provide a networking interface to con-
nect an individual household into a ’green energy’
network.
Learning such Pareto ’curves’ in a broad range
of scenarios of water usage and organizing them in
a knowledge base by different users’ preferences and
diverse water usage scenarios could make it possible
to forsee water individual usage habits over a day and
in the future to set the right trade-offs in an automated
way without interrogating the user and only based on
the obtained knowledge.
The scenario considered in this paper can be also
adapted to ToU double-rate tariffs in the future. For
example, if the night price is lower than the day time
electricity rate (e.g., Economy 7 in UK), then con-
troller can preheat all the water in the period of lower
energy cost.
The future work can be also done on the new type
of user discomfort originating from the tap water flow
acceleration. One can derive a new metric that quan-
tifies user inconvenience from sudden variation of the
water flow. To diminish this discomfort this metric
could be, for example, translated into constraints for
the flow control algorithm.
6 CONCLUSION
In this paper we pointed out a new possibility to im-
prove the efficiency of energy consumption for water
heating by means of the tap water flow rate control
mechanism implemented in conformity with the user
comfort demand. It can be expected that based on
the information about impacts of the offered flow con-
trol solutions for a domestic electric tank water heater
on energy consumption and personal comfort the end-
user can consciously limit the tap flow rate in certain
scenarios of the hot water usage and thereby can gain
energy/money savings.
We introduced a metric that quantifies user dis-
satisfaction with the tap flow rate, the flow discom-
fort model, and extends the thermal discomfort model
presented previously in our works. The flow discom-
fort model has been explicitly utilized in the flow rate
control scheme by means of the multi-objective opti-
mization and its performance has been demonstrated
for the specific scenario of water usage where the user
requests the fixed tap flow rate.
The paper has a special focus on the way the pro-
posed flow control mechanism can be communicated
with the user. By simulating several home WAs we
illustrated a powerful potential of Pareto fronts to
meaningfully group and cross-relate multiplicity of
different individual solutions. Visualized in the user
interface Pareto fronts enable to make focused trade-
offs between the desire to save energy for water heat-
ing and to get the preferred quality of water service.
In addition, the analysis points out that the flow
control step-size has opposite effects on the user flow
rate discomfort and thermal discomfort respectively.
To have a control over the both types of discomfort
the size of the flow control steps should be optimally
chosen.
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