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Understanding usage patterns of electric kettle and energy saving
potential
D.M. Murray
⇑
, J. Liao, L. Stankovic, V. Stankovic
Department of Electronic and Electrical Engineering, University of Strathclyde, 204 George St., Glasgow, United Kingdom
highlights
Time-of-use analysis to motivate kettle usage and consumption prediction.
Identification of households whose kettle usage and consumption is outside the norm.
Mathematical model to estimate water volume from consumed power measurements only.
Quantification of energy savings if a household uses its kettle more efficiently.
Kettle usage and demand prediction using an Adaptive Neuro Fuzzy Inference System.
article info
Article history:
Received 9 December 2015
Received in revised form 20 February 2016
Accepted 13 March 2016
Available online 22 March 2016
Keywords:
Appliance modelling
Appliance use prediction
Energy savings
abstract
The availability of smart metering and smart appliances enables detecting and characterising appliance
use in a household, quantifying energy savings through efficient appliance use and predicting
appliance-specific demand from load measurements is possible. With growing electric kettle ownership
and usage, lack of any efficiency labelling guidelines for the kettle, slow technological progress in improv-
ing kettle efficiency relative to other domestic appliances, and current consumer attitudes, urgent inves-
tigation into consumer kettle usage patterns is warranted. From an efficiency point of view, little can be
done about the kettle, which is more efficient than other methods of heating water such as the stove top
kettle. However, since a majority households use the kettle inefficiently by overfilling, in order to meet
energy targets, it is imperative to quantify inefficient usage and predict demand. For the purposes of scal-
ability, we propose tools that depend only on load measurement data for quantifying and visualising ket-
tle usage and energy consumption, assessing energy wastage through overfilling via our proposed electric
kettle model, and predicting kettle-specific demand, from which we can estimate potential energy sav-
ings in a household and across a housing stock. This is demonstrated using data from a longitudinal study
across a sample of 14 UK households for a two-year period.
1
Ó2016 The Authors. Published by Elsevier Ltd. This is an open access article underthe CC BY license (http://
creativecommons.org/licenses/by/4.0/).
1. Introduction
An electric kettle is an electrical appliance, that has a self-
contained heating unit, for heating water, and automatically
switches off when the water reaches boiling point or at a preset
temperature below 100 °C. It is thus different to the stove top ket-
tle, which is less energy efficient and takes longer to boil the same
volume of water as the electric kettle. In the rest of this paper, we
refer to the electric kettle as kettle only.
The kettle is one of the most used appliances in the United King-
dom (UK) as well as the appliance with the highest rates of owner-
ship; according to UKs Department for Environment, Food and
Rural Affairs 2006 report [1], 97% of UK households own a kettle.
Kettle ownership, and consequently kettle load demand, is also
growing worldwide. For example, in Libya, 42% of homes owned
a kettle in 2013, compared to 8% five years ago, with an estimated
annual energy use of 374 kW h per household [2].
In the UK, more than nine in ten people (90%) use the kettle
every day, with 40% doing this five times a day or more. Thus,
the kettle has become a key domestic consumer. The 2012 annual
electricity consumption of the kettle in the UK was 4489 GW h,
which is roughly 34% of the total consumption attributed to
http://dx.doi.org/10.1016/j.apenergy.2016.03.038
0306-2619/Ó2016 The Authors. Published by Elsevier Ltd.
This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
⇑
Corresponding author.
E-mail addresses: david.murray@strath.ac.uk (D.M. Murray), jing.liao@strath.ac.
uk (J. Liao), lina.stankovic@strath.ac.uk (L. Stankovic), vladimir.stankovic@strath.ac.
uk (V. Stankovic).
1
The open-access REFIT Electrical Load Measurements dataset of the 14 UK
households used in this study can be accessed via DOI 10.15129/31da3ece-f902-
4e95-a093-e0a9536983c4.
Applied Energy 171 (2016) 231–242
Contents lists available at ScienceDirect
Applied Energy
journal homepage: www.elsevier.com/locate/apenergy
cooking [3]. Moreover, the electricity demand from the kettle is
increasing (at the expense of electric ovens and hobs due to
changes in cooking practices and increased oven efficiency) and
according to [3] will surpass, in the UK, the annual consumption
of 5000 GW h by 2030, contributing close to 40% of the overall
cooking electricity demand.
Though, overall, a lower consumer when compared to the elec-
tric heater or washing machine, the kettle is one of the appliances
that has the highest wattage and requires the highest current when
switched on [4]. This is evidenced by high spikes, caused by kettle
usage, in the otherwise low to medium demand profile of a typical
household [5]. Due to the spiky nature of its demand, the kettle can
significantly influence electricity generation and the power distri-
bution network, mainly due to the so-called ‘‘TV pick-up effect”
that manifests itself through significant and synchronised usage
of appliances, such as kettles and microwaves, during TV pro-
gramme breaks [6].
The kettle is also one of the most inefficiently used appliances.
In a survey of 86,000 homes in the UK, by the Energy Saving Trust
[7], it was found that three-quarters of British households admit to
overfilling their kettle when boiling water and are subsequently
wasting GBP68 million each year. Similarly, in Libya [2], over 50%
claim to overfill their kettle. However, both these statistics are
based on interviews, instead of measurements. While kettle usage
is generally assumed to be very regular and non-random [4,8],to
the best of our knowledge, there has been no in-depth study which
analyses patterns of kettle consumption. This is probably because
of the assumption that kettle usage is highly routinized, monitor-
ing kettle usage requires consumer engagement, and that the ket-
tle is not considered a candidate for flexible domestic electricity
demand [3], and as such, not of high interest to demand response
measures.
Nevertheless, a clear trend in increased kettle usage [2,3], lack
of any efficiency labelling guidelines, slow technological progress
in improving efficiency (relative to other cooking appliances),
and current consumers attitudes (86% of people do not choose ket-
tles based on their features, but on looks to match a kitchen design/
already owned products (see [1] and references therein)), all call
for urgent investigation into consumer behaviour patterns with
respect to kettle usage and energy conservation measures.
In this paper, we test the above assumption of regularity in ket-
tle usage, quantify the actual and predicted contribution of energy
consumed by the kettle in a household, and propose a method to
determine energy waste from load measurements only. This is sup-
ported by a longitudinal study comprising a sample of 14 UK
houses, of different occupancy and age groups (e.g., retirees, work-
ing couples, families with children and single occupants), some
energy conscious and others not. The timestamped kettle power
consumption was collected via an appliance-level smart plug mon-
itor that measures active power every 6–8 s [9]. See [10] for details
about the field study.
The main challenge in assessing energy waste due to overfilling
the kettle is measuring fill water volumes in a non-intrusive way,
since it is impractical to measure and record water volume for
every kettle use. This paper overcomes the above problem by
measuring the individual kettle consumption (kW h) and estimat-
ing the water volume from this measurement using mathematical
modelling. In particular, using measurements with different
kettle types, a generic mathematical model is built that relates
the water volume of a kettle, its consumed power and water
temperature.
We demonstrate how power consumption information and
time of use information, together with the proposed mathematical
model, can reveal a household’s behaviour in terms of water over-
boiling and energy wastage, and identify established routines and
usage synchronicity across the monitored households.
Furthermore, we study short-term and long-term load forecast-
ing [11], which is useful for energy feedback, load balancing [12],
effective planning and power plant management [13], demand
response [14,15] and renewable energy systems and energy stor-
age design [16]. Since consumers directly interact with appliances,
appliance-level load forecasting is particularly challenging [14] as
it depends on human behaviour, which is often stochastic and
unpredictable. Moreover, energy efficiency measures and utility
programs affect forecasting which is often a challenge to account
for [17]. Adopting the established Adaptive Neuro Fuzzy Inference
System (ANFIS) [18] prediction tool, we show that kettle usage and
energy consumption can accurately be predicted, short- and long-
term. Using this knowledge, we show how we can predict potential
annual energy savings per household and for an entire housing
stock if energy saving measures were taken.
In summary, the key contributions of the paper are:
Time-of-use analysis to understand patterns of use and its
implications for accurately predicting kettle usage and
consumption.
A method for identifying households whose usage is outside the
norm through understanding energy consumption patterns to
support energy conservation measures.
A mathematical model of the kettle that relates water fill levels,
consumed power, and change in water temperature to estimate
water volume from consumed power measurements only.
Quantification of energy savings if households use their kettle
more efficiently by quantifying overfilling and reboils.
Kettle usage and demand prediction using an Adaptive Neuro
Fuzzy Inference System, which is also used to estimate energy
savings for the next year if current patterns of use are maintained.
The paper is organised as follows. First, we discuss related work
in the literature in Section 2. In Section 3, we present our findings
with respect to temporal and energy usage analysis. In order to
quantify energy waste due to overfilling, we describe our proposed
modelling approach for estimating water volume and the results of
our energy waste analysis in Section 4. Finally, Section 5describes
our prediction of usage and energy consumption methodology and
its application to estimating energy savings if households take on
board energy conservation measures of not overfilling the kettle.
2. Literature review
In this section, we briefly review prior work. We group the rel-
evant literature into three categories: (1) understanding usage of
different domestic appliances; (2) energy usage of the kettle; (3)
appliance-level load prediction. Interestingly, despite the fact that
the kettle has a non-negligible influence on electricity demand,
modelling and forecasting methods to understand and predict
demand, as well as calculating energy-wasteful usage, have not
been analysed in detail so far for this appliance.
Many empirical studies on consumer attitudes and interactions
with energy-consuming appliances have been reported recently,
tackling this issue from consumer study [19], human computer
interaction (HCI) [20], and energy [21,22] angles. For example, tar-
geting autonomous load shifting, in [21], novel generic probabilis-
tic models for wet-appliance usage are proposed that account for
variability of patterns in usage. In [19], based on a longitudinal
study in 29 countries, individual user attitudes towards manual
and automatic dishwashing is considered, with the conclusion that
dishwashers save water considerably more, and providing cleaner
dishes with respect to manual dishwashing.
In [20], interactions with domestic appliances are studied
through a qualitative longitudinal field-work with a sample of 12
households and an online survey, concluding that consumer beha-
232 D.M. Murray et al. / Applied Energy 171 (2016) 231–242
viour is not the result of motivated actions, but instead it is
strongly shaped by external factors. Appliance-level energy-
conserving interaction is analysed with terminology that includes
cutting (powering off when not used or reducing the usage), trim-
ming (using at a lower setting), switching (using a more energy-
efficient device that has slightly different functionality), upgrading
(getting a more-energy efficient appliance with the same function-
ality) and shifting (shifting the use to a different time or place) the
load.
Earlier studies on kettle efficiency are led by energy charities or
government where the emphasis is on assessing overboil, mini-
mum water volumes, and daily/monthly/annual costs based on
average estimates [7]. Indeed, a recent survey [23] conducted
across 2616 households showed that the percentage of households
who admit to overfill their kettle is similar to the percentage of
households who leave their television and computer on standby
for long, but is significantly higher than the percentage of house-
holds who forget to switch off light when they leave a room. Hence,
it is imperative to understand patterns of use, determine a
methodology for accurate assessment of energy savings cus-
tomised to a household and address eco-friendly behaviour when
it comes to the kettle.
Improving usage efficiency and designing eco-feedback [20] to
reduce energy wastage when using the kettle is considered by
the HCI community in [24,8,4].In[24], the effects of using adaptive
aversive and appetitive stimuli to change consumer behaviour is
discussed. Specifically, when the consumers use the correct
amount of water, they are rewarded with a virtual gold star. On
the other hand, when they draw too much water, they receive a
negative reinforcement message. The method has not been tested
in the field. In [8], a kettle prototype is designed, dubbed stroppy
kettle, with a goal of changing bad habits of overfilling the kettle.
The main idea is to impose on the user a punishment task if he/
she is over-filling the kettle. Similarly, recognising that syn-
chronous use of kettle can have significant negative impact on
the grid, in [4], a new kettle design is proposed with a goal of
achieving load management [12,25] and providing users with
immediate feedback. None of these designs have been tested in a
longitudinal study.
We note that none of the above work is focused on capturing
and analysing household’s habits w.r.t kettle usage. An exception
is [26], where kettle usage patterns in the context of assisted living
of people with early dementia was studied. However, focused on
activity recognition, the work in [26] only considers the number
of kettle uses without relating the findings to energy conservation
and eco-behaviour.
Prediction of energy use is crucial in achieving energy conserva-
tion. Many prediction methods have been studied in the past for
forecasting total load in residential settings. For example, in [13],
all load forecasting methods are grouped as engineering, statistical
and artificial intelligence methods, where the latter namely Sup-
port Vector Machines (SVMs) and neural networks, are shown to
be the most accurate methods, but more complex and slower than
statistical methods. In [27], wavelet transform and ANFIS are com-
bined to provide high accuracy hourly prediction of large scale
power system load. In [15], a short-term, day-ahead, demand pre-
diction method for non-flexible loads is developed using cluster-
ing. [28] looks at a number of prediction algorithms including
ANFIS for regional load prediction on a yearly basis for regional
load in Taiwan, concluding that ANFIS is the most effective of the
models trialled. In [29], ANFIS is applied to predict residential
aggregate load profiles.
Appliance load modelling for forecasting has been studied
extensively. See, for example, [30,21,31,5] and references therein,
where different probabilistic models are developed for multi-
state appliances. In [30,5], a high resolution modelling approach
is developed to capture operations of kettle and similar appliances
that have short durations but high impact on distribution network
due to extremely peaky (spiky) nature of their demand. A generic
framework for load forecasting at appliance level was studied in
[14] based on recognising key energy-consuming activities. How-
ever, no performance results are presented. In [17], the effect of
energy efficiency programs on long-term appliance load forecast-
ing for demand response is studied, mainly focusing on lighting.
In [32,33], different machine learning-based and stochastic meth-
ods are developed and compared to predict if a particular appliance
is going to be switched on or off in the near future. We note that
none of the previous approaches estimates the modelling/forecast-
ing accuracy when applied to the kettle, nor quantifies energy effi-
ciency or savings associated with energy-efficient usage of the
appliance.
3. Longitudinal study: analysis and visualisation of patterns of
use
In this section, we test the common assumption that kettle
usage is non-random and predictable (see, e.g., [4,8]) by studying
a sample of 14 UK households, with different occupancy over a per-
iod of about 2 years. We use the appliance-level kettle monitoring
active power measurements from the REFIT electrical measure-
ments dataset [9], using the same House ID, e.g., House 1,2, etc.,
for reproducibility. More details about the study and data collec-
tion tools can be found in [10].
Additionally, we present tools for quantifying and visualising
kettle usage and its energy consumption in one household and
across households using only appliance-level power sensors or
smart metre data at the aggregate level and applying non-
intrusive appliance load monitoring or disaggregating from the
total load [34]. The work presented here builds on our earlier work
[35], which performs an initial analysis of kettle usage across a few
houses without looking into seasonal usage and factors affecting
usage.
This section presents time-of-use patterns of use and energy
consumption trends, trying to identify distinct usage patterns,
household routines and possibly synchronicity between house-
holds to set the stage for the later tasks of estimating inefficient
behaviour and predict consumption due to the kettle.
3.1. Time of use
We first verify that, within a house, patterns of kettle use are
maintained throughout the year, embedded as the households
steady routines, where only the number of kettle uses differ during
weekday/weekends. A kettle use is defined as the number of times
the kettle load data changes from zero to non-zero, representing
each time the kettle was switched. Duration, water volume and
energy consumption are not quantified here.
Fig. 1 shows that across the year the seasonal effect on kettle
usage is minimal, with a general pattern showing slightly
increased usage during winter which agrees with work done in
[36]. We observe, however, that increase in usage occurs during
UK holiday periods July, August, December, and January, when
occupants are at home for longer periods of time. This warrants a
study of weekday/weekend patterns, when occupants have differ-
ent routines due to working/school hours.
Fig. 2 shows the total usage for all 14 houses during October
2014, which is not a holiday period. Fig. 2a shows the trend across
all households of significantly higher usage at 7am, 1pm and 5pm
(lunch is generally taken at 1–2pm and 5pm signifies the end of the
working day). Fig. 2b shows the general shift that can be seen dur-
ing the weekend: uses are more prominent later in the morning,
D.M. Murray et al. / Applied Energy 171 (2016) 231–242 233
and no significant peaks occur signifying more sporadic use of ket-
tle, which, as will be shown in Section 5, affects prediction accu-
racy of kettle usage and consumption.
In Fig. 3 the houses in the study are grouped by their usage
during the weekday: Those with high usage throughout the
day (Houses 2, 5, 17, 19), those with low usage during work
hours (Houses 7, 9, 12, 13, 20), and those which consist of
retired or semi-retired occupants (Houses 3, 4, 6, 8, 11). Each
group has a distinct pattern throughout the day. The houses in
the high usage group all have at least one minor in the house,
whereas those with low usage are less likely to have members
below the age of 18. Retiree households have less of a distinct
pattern with a morning peak later than those in working house-
holds and usage throughout the day. Additionally, the pattern of
usage that continues late into the night for the group of retired
households can be attributed to House 11, which has been
discussed previously in [35].
3.2. Electricity consumption
While the number of uses explains patterns of use, it does not
quantify how much energy each household consumes when using
the kettle, nor identify variations in occupancy and energy waste
due to overfilling the kettle. Table 1 shows the kettle consumption
for each house over the month December 2014. It can be seen that
consumption varies significantly even in households with a similar
occupancy. kW h per use also varies indicating different levels of
water in the kettle. For example, House 9, with close to 0.1 kW h
per use (a relatively high value for a 2-person occupancy), requires
a deeper investigation into their usage habits, to identify why they
fill the kettle significantly more than other households with similar
occupancy.
Fig. 4 shows the energy consumption of each household plotted
against the number of times the kettle was switched on, i.e., the
number of uses. The data is across all recorded months for each
Apr'14 May Jun Jul Aug Sep Oct Nov Dec Jan'15 Feb Mar Apr
Month'Year
0
500
1000
1500
2000
2500
3000
Uses
Seasonal Kettle Usage
All Houses
Fig. 1. Seasonal kettle usage for all 14 houses from April 2014 to April 2015. Each house is represented with a different colour. (For interpretation of the references to colour
in this figure legend, the reader is referred to the web version of this article.)
2
4
6
8
10
4am
4pm
2am
2pm
12am
12pm
10pm
10am
8pm
8am
6pm 6am
(
a
)
Weekday Usage by Hour
2
4
6
8
10
4am
4pm
2am
2pm
12am
12pm
10pm
10am
8pm
8am
6pm 6am
(
b
)
Weekend Usage by Hour
Fig. 2. Average daily usage of the kettle in October 2014 across all 14 houses, by hour.
234 D.M. Murray et al. / Applied Energy 171 (2016) 231–242
household. It can be seen that a clear linear trend is apparent (line
of best fit y¼0:0684x), where 7 houses fall below this fitted line
and 7 are above it. The houses that fall below the line of the best
fit are prime candidates to help understand efficient kettle usage.
On the other hand, House 9 far exceeds the mean consumption.
With respect to the Energy Saving Trust’s findings [7] we could
expect 3–4 houses of the 14 not to overfill the kettle; it can be seen
that, Houses 6, 17 and 19 appear to have kettle usage habits which
do not excessively overfill.
A case study of a household that replaced their standard kettle
with an eco-kettle during the recording period is described in
Appendix A.
3.3. Findings summary
In this section, we confirm that while individual households
have predictable patterns of use, there are weekday/weekend vari-
ations as well as seasonal variations, which we attribute primarily
to holidays rather than weather changes. This findings are in accor-
dance to [22], where it was shown that the usage of three user-
dependent appliances (clothes washer/dryer and dishwasher) does
not depend on the season but is not consistent over weekends and
peak times and have more variations if there are occupants work-
ing from home. Secondly, we show various mechanisms by which
kettle usage and energy consumption can be analysed and visu-
alised, with a case study showing the impact of introducing an
‘eco’ kettle for the purpose of reducing energy consumption.
4. Energy waste estimation
While analysis of kettle usage and associated energy consump-
tion can yield useful insights into patterns of use across a housing
stock and over time, they do not reveal the amount of energy waste
due to overfilling and re-boiling the kettle. In this section we
describe the proposed mathematical modelling method used to
estimate water volume based on measured consumed power, and
then use the proposed model to estimate the amount of energy
waste due to overfilling the kettle.
4.1. Mathematical modelling
The objectives of the proposed mathematical modelling are: (i)
to determine whether there exists one generic model or equation
that can estimate the water volume of a standard or smart kettle
12am 1am 2am 3am 4am 5am 6am 7am 8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm 5pm 6pm 7pm 8pm 9pm 10pm 11pm
Time of Day
0
5
10
15
20
25
30
Uses
High Usage
Retiree Usage
Low Usage
Fig. 3. Usage for all 14 houses grouped by occupancy type. The numbers present the average usage for October 2014 per house in the group.
Table 1
The number of occupants, total electrical consumption, and kettle electrical consumption for all 14 monitored houses. The data are given for December 2014.
House Occupancy Total kW h Kettle kW h Total monthly cost (GBP) kW h per single kettle use % of total energy consumption
2 4(2) 621.45 14.83 1.96 0.062 2
3 2SR 471.17 18.28 2.41 0.072 4
4 2R 270.59 6.87 0.90 0.068 3
5 4(2) 676.58 19.41 2.56 0.073 3
6 2SR 324.74 15.04 1.98 0.060 5
7 4(2) 514.88 8.69 1.14 0.075 2
8 2R 571.73 16.09 2.12 0.067 3
9 2 537.10 23.24 3.07 0.098 4
11 1R 152.51 12.02 1.58 0.072 8
12 3 305.78 19.07 2.52 0.097 6
13 4(2) 317.26 6.09 0.80 0.088 2
17 3(1) 324.57 21.01 2.77 0.062 6
19 4(2) 216.38 9.00 1.19 0.057 4
20 3 291.55 11.65 1.54 0.067 4
4(2) means there are 4 occupants including 2 minors. SR/R refers to (semi-(retired)) occupants. The consumption results are given for December 2014. Total monthly cost
assumes 0.13GBP per 1 kW h.
a
a
Average tariff during field trial.
D.M. Murray et al. / Applied Energy 171 (2016) 231–242 235
using consumed power data only with high accuracy (a smart ket-
tle would include additional heating temperatures 70–100 °C and/
or a keep warm functionality), (ii) determine whether separate
models for standard and smart kettles yield higher relative estima-
tion accuracy, and (iii) assess its relative accuracy compared to the
‘specific heat’ physical model described in [37], where the kettle is
treated as a classic heating element. The work presented here
builds on [35] by producing a more robust model with more exper-
iments, presenting a reproducible equation for the mathematical
model and showing how this model can be used to assess energy
waste in a housing stock.
The physical relationship between volume, temperature and
consumed power for a heating element is given by [37]:
W¼
a
b
D
T;ð1Þ
where Wdenotes water volume (represented in kg where
1 L = 1 kg), ais consumed power in kiloJoules (kJ), bis the specific
heat capacity of water (= 4.19 kJ/kg °C) and
D
Tthe change in tem-
perature after and before heating the water (in degrees Celsius).
Density of the water is encapsulated in the value of specific heat
[38]. We note that physical parameters such as heat capacity and
density do not vary significantly for the temperature range of inter-
est, i.e., from room temperature to boiling, and hence we do not
consider these variations in the equation above.
Initial tests [35] with the physical model of (1) yielded large
error during experimentation with the actual volume (see Table 2).
This motivated the design of a more accurate mathematical model
based on regression analysis [39] using experimental data, while
still maintaining the objective of providing a scalable model that
depends on load measurements, available non-intrusively and at
little cost, and is fit for purpose.
Due to the simplicity of a kettle driven by a heating element,
and our observation that the boil time is nearly linear with respect
to the volume of water, we can reasonably assume a linear rela-
tionship between water volume and consumed power, taking
starting temperature into account. That is:
W
est
¼a
0
þa
1
D
T
meas
þa
2
P
meas
;ð2Þ
where W
est
is the water volume estimation, and
D
T
meas
and P
meas
are
measured temperature difference and measured consumed power,
respectively.
D
T
meas
represents the difference in temperature after
and before switching on the kettle, i.e., the difference between the
temperature of the water in the kettle immediately before heating,
and the temperature immediately after heating. The larger this dif-
ference, the more power will be consumed. Intuitively, lower vol-
umes of water require less power to heat up than larger volumes.
In practice, since we are proposing a scalable, non-intrusive model,
D
T
meas
can be calculated as the difference between 100 °C and room
temperature typical for the time measurements were taken.
a
i
;i¼0;1;2, are constants that need to be estimated to minimise
the error between W
est
and true, measured water volume W
meas
,
which is traditionally solved by linear regression.
Specifically, we tested three linear regression methods: stan-
dard polynomial method [40], locally weighted linear regression
[40] (a ‘memory-based’ method that performs a regression around
a point of prediction using only training data that are ‘local’ to that
point), and the simplest linear interpolation method.
We performed experiments using four non-faulty kettles,
namely 2 standard kettles and 2 smart kettles, measuring the fol-
lowing parameters: consumed power in [kW h], water volume,
starting water temperature, finishing water temperature
(6100 °C). A standard kettle is defined as a kettle that boils water
to 100 °C with no additional ‘boil’ temperatures and no ‘keep
warm’ or additional functionalities, unlike a smart kettle which
allows water to be heated to temperatures less than 100 °C.
280 experiments were carried out, 140 with standard kettles
and 140 with smart kettles. 5/7 of the data was used for training
the model and the remaining 2/7 used for validation of the model.
As a result, three kettle models were developed using surface fit-
ting with the data obtained from the experiments, namely: (1) gen-
eric kettle model that combines smart kettle and standard kettle
measurements, (2) standard kettle model, built with standard ket-
tle data only, (3) smart kettle model, built with smart kettle data
only.
The accuracy of the models is assessed by the root-mean square
error (RMSE) given by:
RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P
N
i¼1
ðW
i
est
W
i
meas
Þ
2
N
s;ð3Þ
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Number of Uses
0
50
100
150
200
250
300
350
Consumption (kWh)
Kettle Usage vs Consumption
H2 H3
H4
H5
H6
H7
H8
H9
H11
H12
H13
H17
H19
H20
Fig. 4. Household consumption plotted against the number of kettle uses together with the fitted line.
Table 2
RMSE for the three kettle models and using Eq. (1).
Linear interpolation Polynomial Locally weighted Eq. (1)
Generic 120.79 94.79 147.67 173.24
Standard 217.32 53.69 153.85 136.75
Smart 74.40 72.64 133.78 203.28
236 D.M. Murray et al. / Applied Energy 171 (2016) 231–242
where W
i
est
;W
i
meas
are i-th estimated water volume and measured in
the testing dataset and Nis the number of measurements in the
testing dataset. The results for N¼80 for the generic model and
physical model in (1) and N¼40 for the standard and smart kettle
models are shown in Table 2.
Note from the table that the RMSE of Eq. (1) [37] is consistently
larger than all other linear models evaluated. The polynomial lin-
ear interpolation method provides the lowest RMSE. As expected,
the general kettle model performs worse than the bespoke stan-
dard and smart kettle models. Thus, the generic model should be
used only if estimating the water volume of a kettle, whose type
is unknown. This can happen if the type of kettle is unspecified
during an appliance survey.
The resulting mathematical relationship using the best-
performing polynomial linear method is defined as:
WðLÞ¼a
0
a
1
D
Tþa
2
P
meas
;ð4Þ
where the value of the coefficients a
0
;a
1
and a
2
are shown in
Table 3.
4.2. Estimating energy wasted due to overfilling and reboiling
Equipped with the above model, we can estimate the amount of
wasted energy due to overfilling the kettle using only the collected
consumed power measurements, P
meas
. Since, during the field trial,
all households, apart from House 3, as discussed in Appendix A,
were using standard kettles, the standard kettle model (4) is used
to quantify waste due to overfilling.
First, we use kernel density estimation [41] to help better visu-
alise the water filling patterns of the households. Kernel density
estimation
2
is a non-parametric way to estimate probability density
function of a random variable, and therefore does not assume an
underlying distribution. It helps to visualise a higher number of uses
for a particular value(s) of the random variable by creating a bump
(s). Fig. 5 shows our results for five houses where the random
variables are energy consumption and water volume estimated in
the kettle per use. The negative volume scale represents re-boils,
i.e., when the occupant uses the kettle before the water has cooled
to room temperature. This is determined when a kettle use happens
within 2 min of a previous use or its water volume is expected at less
than 200 ml.
Obviously, different households have different preferred levels
of water per boil, and consequently, consume differently per single
kettle use. Houses 6 and 19 have a similar water-filling pattern: a
very narrow boil range between 0.05–0.075 kW h; House 19 has a
higher percentage of re-boils (hence, the second 0.025 kW h peak).
The other end of the spectrum is House 12, peaking at more than
0.1 kW h with a wide bell curve on each side. This suggests that
this house is the least efficient house in the survey group. House
9 has two peaks of relative magnitude, 0.05–0.075 kW h and
0.125 kW h, respectively. This wide range of consumption per
usage suggests that the kettle is filled with little thought as to
the purpose. House 5 is between the two extremes no significant
peak, but drops after 0.1 kW h at an equivalent rate to Houses 6
and 19, suggesting a slightly more economical usage with compar-
ison to Houses 9 and 12.
It can be seen from Fig. 5b that House 6, which has been shown
in the previous section to be an economical kettle user, has the
lowest number of uses where the water level has been above 1 L
and the usage peaks at just under 0.5 L. Similarly, House 9 has been
shown to be one of the less economical users (see Table 1): Two
distinct peaks are visible, one at 500 and 1250 with a slow tail
off. House 19 which has the highest reboil peak, with 37% of all
recorded uses estimated as re-boils consuming 15.14 kW h. House
12 which has a much larger number of uses has the lowest peak
where 22% of uses are re-boils accounting for 10.77 kW h of
consumption.
From Fig. 5, we can estimate how much energy could be saved
assuming that the household cuts down on overfilling their kettle,
as well as re-boils and assume a minimum of 500 mL (many kettles
minimum fill), 275 mL per adult occupant for each household and
138 mL for each minor in the house. As an example, for House 9
which has 2 adult occupants, working from the assumption that
a usage is minimum 500 mL, for two people ideal water volume
will be 550 mL. Over the entire study period, House 9 had a
recorded 3441 uses of which 1497 were above 1000 mL. This
accounts for a consumption of 220.45 kW h of a total
313.48 kW h. The average kW h cost for 525–575 mL is
0.08 kW h. If all of the uses above 550 mL were reduced to
550 mL a saving of 102.13 kW h could have been made over the
18 months monitored for House 9, or 68.09 kW h per year. Simi-
larly, House 12 which has 3 occupants should fill kettle to around
825 mL. House 12 has 2755 recorded usages with 907 of those
usages being greater than 825 mL. This accounts for 113.97 kW h
of a total 199.18 kW h recorded over the study period. Reducing
these overboils to the maximum 825 mL could result in an annual
saving of around 17.45 kW h.
The results for all 14 houses are summarised in Table 4,
where estimated annual savings that could be obtained via more
economical usage habits are up to 92 kW h per household. While
the consumption difference may be insignificant to an individual
household, it is significant for the whole housing stock, with
clear impact on electrical demand and regional carbon footprint.
Indeed the total consumption of the housing stock in our
modest sample study adds up to 2181 kW h, which is not
insignificant.
5. Demand prediction
As shown in Section 3, kettle usage patterns are part of estab-
lished domestic daily routines (e.g., a high likeliness of usage early
in the morning), and hence it is natural to assume that they can be
accurately analytically predicted. In this section we present our
findings on kettle use and energy demand predictability. We note
that predicting kettle demand, to the best of our knowledge, has
not been studied before.
By predicting kettle demand, one can quantify the amount of
energy that could be saved (annually or monthly) if usage patterns
change, for example, if the kettle is not overfilled. Moreover, appli-
ance demand prediction is useful in time-use studies to under-
stand routines and practices in the home.
To predict usage patterns we look at two different variables,
namely energy consumption and uses. We adopt adaptive
network-based fuzzy inference systems (ANFIS), which is well
established for demand prediction and particularly suitable to
this problem since, as has been shown previously, kettle data
tend not to have a large variance, e.g., uses across any given
hour will not vary greatly per household regardless of current
day or month.
Table 3
Kettle model coefficients for (4).
Generic Standard Smart
a
0
1.025 1.244 0.905
a
1
0.01595 0.02209 0.01401
a
2
12.34 14.54 11.82
2
A kernel is a type of probability density function which must be even.
D.M. Murray et al. / Applied Energy 171 (2016) 231–242 237
5.1. ANFIS demand prediction methodology
ANFIS is a type of artificial neural network that is based on the
Takagi–Sugeno fuzzy inference system [18], suitable for time-
series prediction. In our system we first use Fuzzy C-Means Clus-
tering (FCM) [42] to extract rules from the input data. Once FCM
has generated a fuzzy inference systems (FIS) structure [18],itis
then trained for 20 epochs or until no further improvements can
be made adjusting the initial rules.
In particular, to predict the consumption or usage in the next
hour ðtþ1Þthe FIS structure was generated using the following
parameters:
weekdayðtÞ;xðt24Þ;xðt23Þ;xðt22Þ;xðt2Þ½
where xis a vector of the consumption(uses) in kW h/uses at time t
[in hours], e.g., xðt24Þis the consumption(uses) during the hour
which is 24 h before to the current hour. weekdayðtÞis the current
weekday where Sunday is 1 and Saturday is 7.
These variables were chosen by using a sequential search
method to find which xðtnÞlend the most weight to prediction.
As with any prediction method, ANFIS is limited by the quality of
the historical data provided. Additionally, consumption prediction
is affected by variation in water fill level, meaning that signifi-
cantly higher usage in the month prior, e.g., holiday month, will
result in an over prediction. Usage prediction is greatly affected
by reboils and as such when they are included as input data cause
over prediction; thus, since the consumption effect of reboils is
small, they are not considered as a use for prediction.
5.2. ANFIS accuracy
Energy consumption prediction as the combined hourly predic-
tions for each month over the yearly period for House 20 is shown
in Fig. 6. A good agreement with the true consumption can be
observed from the graph. The most significant error is in May,
due to a sudden jump in consumption w.r.t the previous month.
Table 5 shows the results for all houses expressed by RMSE.
RMSE is calculated between true consumption values [kW h] and
predicted. A lower RMSE will show a more predictable pattern of
usage while higher RMSE will show more erratic patterns of use.
It can be seen from the table that for most houses annual con-
sumed energy prediction error is in the 2–3 kW h range. The
exception is House 13 which shows a considerable error; this is
explained by their considerably higher than usual usage during
the months of Sept’14 and Feb’15.
0 0.05 0.1 0.15 0.2 0.25
Consumption (kWh)
0
5
10
15
Density
Kettle Consumption per Use
Kernel Density Estimate
House 5
House 6
House 9
House 12
House19
(a) Energy consumption per use
0-1000 -500 500 1000 1500 2000
Volume (mL)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Density
×10
-3
Kettle Volume per Use
Kernel Density Estimate
House 5
House 6
House 9
House 12
House 19
(b) Water volume per use
Fig. 5. Kernel density estimation of kettle consumption and water volume per use for five houses. The negative volume scale represents re-boils.
Table 4
Potential energy savings if householders did not overfill their kettle.
House Occupants Kettle consumption
(kW h)
Household reduced fill
volume (mL)
Consumption above
volume (kW h)
Savings per year
(kW h)
Savings per year
(GBP)
2 4(2) 210.10 825 115.07 21.66 2.98
3 2SR 170.07 550 126.31 41.22 5.67
4 2R 95.88 550 59.55 10.97 1.51
5 4(2) 199.21 825 100.45 19.85 2.73
6 2SR 207.27 550 110.51 24.86 3.42
7 4(2) 72.84 825 31.65 6.56 0.90
8 2R 184.99 550 145.44 36.67 5.04
9 2 248.42 550 215.81 92.22 12.68
11 1R 157.58 500 98.44 30.83 4.24
12 3 162.60 825 93.63 21.33 2.93
13 4(2) 90.73 825 61.71 10.19 1.40
17 3(1) 166.49 550 107.97 26.00 3.58
19 4(2) 95.07 825 29.68 4.57 0.63
20 3 120.19 825 19.06 2.38 0.33
238 D.M. Murray et al. / Applied Energy 171 (2016) 231–242
5.3. Cost saving estimation
Using the proposed ANFIS method we can estimate possible
savings that could be made if kettle usage is adjusted to the recom-
mended level defined in Table 4. To do this, we first predict the
number of uses of kettle and multiply that by the power usage cal-
culated via Eq. (4) for recommended water levels for the given
occupancy (Table 4). This is compared with the energy consump-
tion if the kettle use behaviour remains unchanged (that is, the
household continues to use the same water levels). The difference
between these values is then the estimated savings that could be
made assuming that every kettle usage is filled to the recom-
mended level.
Fig. 7 shows results for House 9, which was identified before as
the least economical kettle. The results for the other houses in the
study are shown Table 6.
In Table 6 predicted savings in kW h can be seen for the period
April 2014–April 2015. House 20 can be seen to have a negative
value associated with the saving. This can be explained by refer-
ence to House 20’s economical usage habits. Indeed, House 20
must have many boils under their ideal fill level of 0.825L that
assumes that all boils are for three people. Furthermore, across
all households, the overall savings add up to a significant
548 kW h, which averages to 40 kW h per house.
6. Conclusion
This paper presents scalable tools for predicting and quantifying
energy consumption due to the kettle and inefficient use due to
overboiling using only widely available smart metre data. This is
enabled by our proposed mathematical model that estimates water
4
5
6
7
8
9
10
11
12
13
14
Consumption (kWh)
Predicted Monthly Consumption
House 20
Actual
Predicted
Apr'14 May Jun Jul Aug Sep Oct Nov Dec Jan'15 Feb Mar Apr
Month'Year
Fig. 6. Predicted kettle consumption, predicted hourly and summed.
Table 5
RMSE of hourly prediction summed over 12 months.
House 2 3456789111213171920
Hourly energy consumption 3.51 3.33 1.79 3.98 2.85 1.79 2.13 2.46 2.21 2.09 12.38 3.46 2.02 1.58
Apr'14 May Jun Jul Aug Sep Oct Nov Dec Jan'15 Feb Mar Apr
Month'Year
8
10
12
14
16
18
20
22
24
26
Consumption (kWh)
Predicted Monthly Consumption
House 9
Actual
Predicted Ideal
Fig. 7. Predicted consumption without overfilling for House 9.
D.M. Murray et al. / Applied Energy 171 (2016) 231–242 239
fill levels of the kettle from the consumed power measurements.
The proposed methods are based on regression analysis and
ANFIS-based demand prediction.
Time of use analysis confirms well-defined patterns of use with
respect to weekdays during standard ‘‘office hours”, pattern varia-
tion depending on type of occupancy and general daily schedule,
holiday periods and minor seasonal variation. Specifically, our
analysis shows that kettle usage patterns are regular at peak times
(morning, evening around dinner) and mainly sporadic otherwise
during the day.
Additionally, we show quantitatively, in-line with
previous studies, that a significant percentage of households do
overfill their kettle. Another factor is reheating water soon after
it has boiled. In these cases households that appear not to overfill,
based on the number of occupants, waste energy on reheating or
reboiling.
We demonstrate that due to well-defined patterns of use, it is
possible to accurately predict kettle usage at a large scale using
only smart metre readings, which could be of interest to network
operators since synchronous kettle usage can have negative effects
on the grid. An additional application of our proposed tools is to
predict energy savings if water filling patterns change through,
for example, more efficient behaviour of filling to ideal levels.
The methods can also be used to enrich customer energy feedback
and provide retrofit advice; an example is shown in Appendix A,
where detailed feedback is provided to a householder to quantify
energy savings incurred when they replaced their standard kettle
with an ‘eco’ kettle.
Acknowledgements
This work has been carried out as part of the REFIT project (‘Per-
sonalised Retrofit Decision Support Tools for UK Homes using
Smart Home Technology’, Grant Reference EP/K002368/1/1). REFIT
is a consortium of three universities – Loughborough, Strathclyde
and East Anglia – and ten industry stakeholders funded by the
Engineering and Physical Sciences Research Council (EPSRC) under
the Transforming Energy Demand in Buildings through Digital
Innovation (BuildTEDDI) funding programme. For more informa-
tion see: www.epsrc.ac.uk and www.refitsmarthomes.org.
Appendix A. Effect of substituting an ‘eco’ kettle for a standard
kettle
House 3 introduced a vacuum(eco) kettle as an energy saving
measure during our study (Winter 2013 - Spring 2015). The vac-
uum kettle keeps water hot for longer, thus potentially reducing
the number of uses. We can therefore look at their usage before
and after the change to show the effect of usage and energy con-
sumption of this new kettle.
The total uses per hour between the standard and vacuum ket-
tle for the same household can be seen in Fig. 8. The standard kettle
usage was much higher at 7am compared to the vacuum kettle.
This can be attributed to the fact the vacuum kettle will be used
once with a large amount of water and retain that heat throughout
the hour. This pattern can also be seen at 3 pm in 2013 when there
were uses in the following two hours. In 2014, the following two
Table 6
Yearly predicted savings for the period April 2014–April 2015.
House 2 3 4 5678 91112131719 20
Predicted savings
(kW h)
8.92 62.9 10.34 6.71 33.56 16.60 54.74 108.00 1.47 18.30 71.02 130.27 45.84 20.26
Predicted savings
(GBP)
1.23 8.66 1.42 0.92 4.61 2.28 7.53 14.85 0.20 2.52 9.77 17.91 6.30 2.79
10
20
30
40
4am
4pm
2am
2pm
12am
12pm
10pm
10am
8pm
8am
6pm 6am
Uses per Hour
House 3 - December 2013
(a) Standard kettle
10
20
30
40
4am
4pm
2am
2pm
12am
12pm
10pm
10am
8pm
8am
6pm 6am
Uses per Hour
House 3 - December 2014
(b) Eco vacuum kettle
Fig. 8. Standard and eco kettle usage in House 3 over the month of December 2013 and 2014, respectively.
240 D.M. Murray et al. / Applied Energy 171 (2016) 231–242
hours have significantly less usage; the hour immediately after has
a much smaller, and the following hour slightly more, possibly
attributed to reheats where the water is not considered hot enough
for the drink being prepared.
Fig. 9 shows the trend in relative energy consumption before
the vacuum kettle was introduced in April 2014, while the vacuum
kettle was used and after the vacuum kettle was removed in late
January 2015. Consumption was lower in the period when vacuum
kettle was used.
Table 7 shows that the eco-kettle has significantly fewer num-
ber of uses and therefore the associated cost has been reduced by
close to GBP0.70 in the comparative months of December. Thus,
the potential for annual savings by replacing a standard kettle with
a vacuum kettle is around GBP8.00. This represents close to a 50%
saving if we assume 1542 kettle uses per year, with an assumption
of 0.11 kW h per use based on heating 1 L of water, resulting in a
cost of GBP16.90.
3
The initial cost of the eco kettle, however, is
around GBP80, therefore there is a significant period of time before
the kettle will be cost effective.
Feedback: The residents of House 3 were provided with the
above visual feedback, along with textual explanation of the find-
ings. A survey was completed prior to feedback to assess the resi-
dents thoughts. The survey revealed a number of traits about the
household. The residents were committed to being eco-friendly
and were positive about buying other products aimed at reducing
energy. They believed that they had changed their habits signifi-
cantly as they actively incorporated the vacuum kettle into their
routine.
As shown above, this can be seen in the comparisons made, in
both usage and water consumption which led to a more economi-
cal usage style. They also made a note of the fact that they tried to
avoid re-heating water and this is backed by the fact that only 7%
of their kettle usage is within a 5-min window of a previous usage.
The household stopped using this vacuum kettle due to a fault,
which once fixed, never made it back into daily usage. Interest-
ingly, this was not due to any effects on performance, but due to
the noise the kettle made, which was annoying to the occupants.
The feedback, however, was well received and the residents
believed that this would be of benefit, and expressed that a
monthly breakdown of appliance usage is beneficial toward sup-
porting their efforts towards being eco-friendly.
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