Enhancing User Comfort Models for Demand Response Solutions for

Domestic Water Heating Systems

Alexander Belov

, Alexandr Vasenev

, Paul J. M. Havinga

and Nirvana Meratnia

Pervasive Systems Research Group, University of Twente, Enschede, The Netherlands

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

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 ﬁxed 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):

= P

+ P

− P

loss

(1)

where M is the water mass in the tank, C is speciﬁc

temperature of water, P

is the thermal power supplied

by the heating elements, P

and P

are cold water

inﬂow and hot water outﬂow of the tank, and P

loss

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

+ P

cw2

˙m

= ˙m+ ˙m

(2)

where P

is the tap water thermal power demanded by

the user, P

is the power ﬂow from the tank, P

cw2

cold water from the main controller, and ˙m

, ˙m, ˙m

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

(t), and the cold

water temperature T

at every moment of time:

k =

˙m

(t) − T

T(t) − T

(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]

0 1 2 3 4 5 6 7

Electric Consumption, [kWh]

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

> (P

− P

loss

)/[C(T

− T

)] leads to the de-

crease of temperature inside the WH as shown in Fig.

2. As a result, the actual tap water temperature T

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

t, [min]

T, [C]

Tank Temperature

Tap Water Temperature

0 1 2 3 4 5 6 7

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

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.

˙m

∑

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

, ˙m

cw,i

},∀i ∈ N, where T

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]

0.4

0.8

1.2

1.6

2.4

2.8

3.2

3.6

Tank Temperature

Electric Consumption

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

in the period

∆t

pre

can be expressed as:

(∆t

pre

) = P

∆t

pre

αP

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

= min[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

(t)

represented earlier in Section 2.3 by incorporating the

individual discontent function F

˙m

. The discontent

function F

˙m

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

˙m











0 , if ˙m

d, i

∈ ∆ ˙m

d, comf

;

˙m

d, i

+ β

, if ˙m

d, i

∈ ∆

−

tol

;

˙m

d, i

+ β

, 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

< 0,α

> 0,β

,β

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:

˙m

∑

i=1

˙m

(7)

where F

˙m

is the user discontent level reached at step

i; A

˙m

speciﬁes the area resulted from the ﬂow ˙m

d, i

deviation from the comfort zone ∆ ˙m

d, comf

during step

The second objective function can be formalized

as F

= min[D

˙m

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

and

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.

Volume,

Estimated

Flow

Rate,

Flow

Range,

[L]

[L/min] [L/min]

Wash Hands

0.7 ... 7.5 6 2 ... 9

Dishwashing

38 ...75 9 6 ...25

Shower

32 ...225 15 8 .. . 25

Bath tap, running water.

Kitchen tap, running water.

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,

[

◦

0.5

[10,12] [40,45]

7 [8,12]

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

shown in Fig. 10.

Since the ﬂow rate discomfort D

˙m

depends on

the size of the control step (via term A

˙m

in (7), we

also estimate the effect of altering the step size on

(∆t

pre

) and D

˙m

. In addition, we show how D

˙m

affects the thermal discomfort D

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

(∆t

pre

) as a function from the ﬂow rate discom-

fort D

˙m

. The discomfort is shown in percentage as a

share of the maximum D

˙m

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

The bar exhibits these values in the following format

[ ˙m

d, min

, ˙m

d, max

],∆t

, which is the minimum and the

maximum ﬂows reached during the WA and the dura-

tion of D

˙m

. The two sequential solutions from Fig.

11(b) that have different D

˙m

and equal E

(∆t

pre

) are

plotted in Fig. 12.

The inﬂuence of the control step size on the ﬂow

discomfort D

˙m

is demonstrated in Fig. 13. The ther-

mal discomfort D

has been calculated for every solu-

tion on Pareto front of the considered WAs. The con-

nection between two different types of discomfort, D

and D

˙m

, 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

min

] and discom-

fort duration ∆T

DISC

speciﬁed in the bar. We also show

how the relation between D

and D

˙m

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

at the cost

of the increased 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

t, [min]

T, [C]

Tank Temperature

Tap Water Temperature

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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

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

10%, (b) D

˙m

= 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

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

results in a steep jump of the

resulting tap water ﬂow rate ˙m

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

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

and E

(∆t

pre

), it has an negative

effect on the thermal discomfort D

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

. Considering the contrary effects of the

step size on the two types of discomfort and E

(∆t

pre

)

a compromise between D

˙m

and D

can be achieved

by incorporating D

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

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

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

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

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, [%]

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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