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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>P. Andreas Gunkel, H. Klinge Jacobsen, C.-M. Bergaentzlé, F. Scheller, F. Møller Andersen,
Variability in electricity consumption by category of consumer: The impact on electricity
load profiles, International Journal of Electrical Power &amp; Energy Systems</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.1016/j.eneco.2021.105341</article-id>
      <title-group>
        <article-title>Back-filling Missing Data When Predicting Domestic Electricity Consumption From Smart Meter Data</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Xianjuan Chen</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Shuxiang Cai</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Alan F. Smeaton</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Insight Research Ireland Centre for Data Analytics, Dublin City University</institution>
          ,
          <addr-line>Glasnevin, Dublin 9</addr-line>
          ,
          <country country="IE">Ireland</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>School of Computing, Dublin City University</institution>
          ,
          <addr-line>Glasnevin, Dublin 9</addr-line>
          ,
          <country country="IE">Ireland</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2022</year>
      </pub-date>
      <volume>147</volume>
      <issue>2023</issue>
      <fpage>439</fpage>
      <lpage>448</lpage>
      <abstract>
        <p>This study uses data from domestic electricity smart meters to estimate annual electricity bills for a whole year. We develop a method for back-filling data smart meter for up to six missing months for users who have less than one year of smart meter data, ensuring reliable estimates of annual consumption. We identify five distinct electricity consumption user profiles for homes based on day, night, and peak usage patterns, highlighting the economic advantages of Time-of-Use (ToU) tarifs over fixed tarifs for most users, especially those with higher nighttime consumption. Ultimately, the results of this study empowers consumers to manage their energy use efectively and to make informed choices regarding electricity tarif plans.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
    </sec>
    <sec id="sec-2">
      <title>2. Background and Context</title>
      <sec id="sec-2-1">
        <title>2.1. Smart Meters</title>
        <p>
          Smart meters are advanced electronic devices designed to measure both the amount of electricity
exported to the grid and imported from the grid by a domestic or business customer. They ofer
consumers and energy providers detailed and up-to-date information on energy consumption compared
to traditional meters by eliminating the necessity for approximate meter readings [
          <xref ref-type="bibr" rid="ref3 ref4">3, 4</xref>
          ].
        </p>
        <p>
          The interval for metering and recording the consumption varies within the European Union (EU)
from 15 minutes to 2 hours, depending on the country [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ] and in Ireland the set interval is 30 minutes,
uploaded at the end of each day. Smart meters facilitate demand-side mechanisms such as ToU tarifs
wherein consumers are charged diferent tarif rates based on various timeslots of the day. Higher rates
are typically applied during peak demand, while lower rates are employed during of-peak periods.
Smart meters enable customers to select their cheapest tarif from an energy supplier and then enable
energy suppliers to ofer more comprehensive insights, including information on the total energy
consumption and categorised appliance usage throughout the household. Overall, they contribute to
reducing carbon emissions and fostering the development of a more sustainable energy system [
          <xref ref-type="bibr" rid="ref5 ref6">5, 6</xref>
          ].
        </p>
        <p>
          As illustrated in Figure 1, thirteen member states in the EU achieved a smart meter roll-out rate
exceeding 80% in 2022, whereas ten member states had rates below 20% [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ]. In Ireland, ESB Networks is
in the process of upgrading electricity meters nationwide and has announced the successful installation
of 1.5 million smart meters in homes, farms and businesses across every county in Ireland in November
2023 [
          <xref ref-type="bibr" rid="ref1">1</xref>
          ]. At the time of writing, the number of installations had risen to 1.8 million
        </p>
      </sec>
      <sec id="sec-2-2">
        <title>2.2. The Irish Energy Market</title>
        <p>
          The electricity sector in Ireland has undergone a paradigm shift, transitioning from a regulated monopoly
to a deregulated competitive market [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ]. Before the 1999 Act and the introduction of a supplier licensing
regime, ESB held a monopoly on electricity retail supply but from February 2005 liberalisation measures
empowered all Irish electricity consumers to choose their preferred suppliers [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ]. This initially restricted
ESB’s ability to set retail prices independently, efectively diminishing its control over the market. As
consumer switching activity reached a satisfactory level deemed by the Commission for Regulation
of Utilities (CRU), these restrictions were progressively lifted for business and domestic consumers in
2010 and 2011. In 2012, ESB’s retail division re-branded as Electric Ireland. By 2022, Electric Ireland
dominated the domestic electricity market in Ireland with a 41% share [
          <xref ref-type="bibr" rid="ref9">9</xref>
          ].
        </p>
        <p>
          The deregulation of the Irish electricity market was positively received by both consumers and
suppliers. This restructuring aimed to enhance consumer choice, lower retail prices, and introduce
innovative products. Consumers became more engaged leading to a better understanding of energy
costs and encouraging conservation eforts. The influx of competitive suppliers provided more choices
and attractive pricing structures, allowing them to cater to unique customer needs and diferentiate
themselves by providing innovative services and benefits. The Consumer Association of Ireland echoed
these sentiments, applauding the move as a “win-win situation for suppliers and consumers" [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ].
        </p>
        <p>
          The Commission for the Regulation of Utilities (CRU) functions as Ireland’s independent regulator
for energy and water, established in 1999 under the Irish Government’s policy and framework [
          <xref ref-type="bibr" rid="ref11">11</xref>
          ]. The
CRU’s oversees energy networks and promotes the use of renewable energy, enforces quality standards,
fosters competition, and provides consumers with information and tools for dispute resolution, and
it regulates gas, petroleum, and electrical contractors. It holds the authority to monitor and ensure
that every licensed electricity supplier adheres to the terms specified in its supply license which cover
aspects such as billing, disconnection, marketing, complaints handling, prepayment meters, and the
treatment of vulnerable customers.
        </p>
        <p>There is a list of all energy providers authorised by the CRU to furnish electricity and gas within the
retail energy market in Ireland [12]. Presently, 13 energy suppliers serve the Irish Electricity market,
catering to a population of 1.84 million households [13]. These are Arden Energy, Bord Gáis Energy,
Ecopower, Energia, Electric Ireland, Flogas, Glow Power, Pinergy, PrePayPower, Yuno Energy Ltd,
SSE Airtricity, Community Power, and Water Power. In total, they provide more than 60 tarifs for
customers with smart meters as well as diferent fixed standing charge amounts depending on whether
the household location is urban or rural.</p>
      </sec>
      <sec id="sec-2-3">
        <title>2.3. Electricity Consumption Profiles</title>
        <p>Many studies have investigated domestic electricity consumption profiles across the world and one
line of research has explored the relationship between the fundamental characteristics of households
and their electricity usage patterns. Studies reported in [14, 15] utilising electricity consumption data
from Danish households revealed that heat pumps, electric vehicles (EVs), and dwelling types exert
significant influence on consumption levels, while socio-economic factors like occupancy, dwelling area,
and income have minimal impact. Additionally, Munkhammar [16] discovered that houses equipped
with EV charging predominantly see an increase in electricity usage during the evening while research
in Germany [17] and Australia [18] demonstrated that households with photovoltaic (PV) systems tend
to have increased electricity consumption.</p>
        <p>The analysis of consumption data has included statistical profile analysis and clustering for profile
extraction [19]. Multiple studies [20, 21, 22, 23] have evaluated various clustering algorithms and
found K-means has a consistent ability to yield superior results in this context. These studies have
also emphasised the importance of determining the appropriate number of clusters and we build on
the lessons and conclusions from this previous work in our use of K-means to cluster our used into 5
profiles.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Experimental Setup</title>
      <sec id="sec-3-1">
        <title>3.1. Data Collection</title>
        <p>The data collection phase for this study was conducted from January 2024 to June 2024. During this
period, two categories of data were gathered: electricity tarif plans from energy suppliers and smart
meter data from households.</p>
        <p>The tarif plan data were obtained directly from the oficial websites of 10 of the 13 energy suppliers.
We excluded 3 oficial suppliers because their market penetration was small. As of June 2024, irrespective
of whether the household location is urban or rural, 58 unique electricity tarif plans were then available,
divided into either fixed-rate or time-of-use (ToU) tarif plans. Specifically, 17 fixed-rate plans provide a
constant price for electricity regardless of the time of day, while 41 ToU plans vary the price based on
the time of consumption and this includes both day/night and smart tarifs. The tarif plan details on
the websites are updated periodically, influenced by the energy market thus checks on the tarifs are
performed every two weeks by manually visiting the oficial websites.</p>
        <p>ESB Networks who provide and maintain the electricity generation and distribution, allows customers
to download their own smart meter data. Customers register on the ESB Networks website using their
MPRN number and download a CSV file that includes all their electricity imports plus exports (if they
micro-generate) from the installation date of their smart meter up to the previous day. This file is
referred to as an HDF file, with a sample shown in the table. 1.</p>
        <p>Data from smart meters installed in households and businesses was collected through a questionnaire.
This included questions about respondents’ dwelling location (urban or rural) in order to determine
which fixed-rate standing charge applies. Users uploaded their HDF files as downloaded from the ESB
Networks website and in return received an email containing estimates of their annual bill across all
available tarif plans in the market, based on their own past electricity consumption.</p>
        <p>The service was released publicly on 31st January 2024 with ethics approval from the School of
Computing ethics approval board. By 15th June 2024, it had received 193 responses and uploads,
representing 113 unique users. Some users uploaded their HDF files multiple times to obtain more
recent feedback as tarifs changed over time. For these users, all data entries from the same MPRN were
combined by taking their earliest and latest end dates. The collected data comprises 127 million data
points across these 113 distinct users.</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Data Cleaning</title>
        <p>All smart meter data from users were trimmed to fall into the period from midnight on 1st May 2023,
to midnight on 1st May 2024, as there was significant variation in the duration of uploaded HDF file
records for each user, ranging from over two years to less than one month.</p>
        <p>HDF files downloaded from the ESB Networks website had occasional missing data which were
sporadic and unpredictable, with the average deviation from the expected record count across all users
being less than 0.43%. The irregularities resulted from factors including network transmission problems,
power outages, and other unidentified issues. For monthly records, if the missing data exceeded 10% of
the month’s duration, the record was excluded from our dataset.</p>
      </sec>
      <sec id="sec-3-3">
        <title>3.3. Data Overview</title>
        <p>After data cleaning, there were 107 users whose records covered at least one full calendar month. Among
these, only 24 users had complete data for all 12 months because the smart meters for the others had
been installed only within the previous 12 months. Such users are usually keen to use their smart meter
data to find the best or cheapest tarif at the earliest possible opportunity, so are not willing to have to
wait a full year after installation. Consequently, there is a real demand for predicting annual energy
usage based on only partial data, as discussed later. Approximately 78% of our users have HDF data
spanning more than 6 months. The distribution of data durations for these users is shown in Table 2.</p>
        <p>Observing the average consumption of all our users over the 12 calendar months reveals a trend
displayed in Figure 2. During the summer and warmer months from May to September, the consumption
lfuctuates around 377 kWh per month and peaks at approximately 740 kWh in January. The cold Winter
months from February to April still maintain a relatively high level of consumption, averaging around
627 kWh. The dip for February is because it has fewer days than other months.</p>
        <p>Because of the varying durations in HDF records and the clear variation in usage based on seasonality,
an annual consumption for those users who have missing HDF data as measured in months, cannot be
accurately calculated as an average monthly consumption multiplied by 12. Therefore, in the following
analysis of annual consumption, only the 24 users with complete data spanning the entire 12-month
period are included in summary Table 3. While the sample size is relatively small, the data presented,
influenced by improving living standards, challenges the accuracy of the CRU’s recommended typical
annual electricity consumption figure of 4,200 kWh, which was announced in 2017 [ 24] and on which
all comparator websites for energy costs, including those regulated by the CRU such as bonkers.ie and
switcher.ie, are based.
An analysis of data from all 107 users provides insights into the broad spectrum of electricity
consumption behaviours. Figure 3 shows the ratios of electricity used across the 3 standard daily ToU timeslots
for these 107 users. Here we see a notable portion (70) of these users display a trend of higher energy
use during daytime, while 37 users show increased consumption patterns at night.
This analysis illustrates the need for a more precise and personalised estimation of households’ electricity
consumption when selecting tarif plans, rather than relying on the CRU’s stated annual domestic
electricity consumption figure of 4,200 kWh.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Methodology</title>
      <p>Users with complete HDF records spanning all 12 months had their past electricity usage calculated,
and their estimated electricity bills for the subsequent 12 months were computed based on all available
tarif plans. Here we assumed usage patterns would not change and that consumption from the previous
year would be the same as for the subsequent year. For users with HDF records covering fewer than 12
months, a methodology was devised to estimate their electricity usage for the missing months with the
collected dataset. This enabled the prediction of annual bills for these users, across diferent tarif plans.</p>
      <p>The overall methodology workflow is displayed in Figure 4, including profile extraction, electricity
usage prediction, evaluation and tarif plan comparison.</p>
      <sec id="sec-4-1">
        <title>4.1. Profile Extraction</title>
        <p>Our 107 users’ HDF records were segmented into 12-month bins. For each month, the total usage was
calculated for each of three diferent daily timeslots as used in ToU tarifs: day (8:00-17:00 &amp; 19:00-23:00),
night (23:00-8:00), and peak (17:00-19:00). The average monthly usage for the three time periods were
then calculated across the users. The monthly usage ratios for these periods were calculated relative to
the total 12-month usage creating a series of data for each user, consisting of 36 ratios that sum to 1.
Users were clustered using K-means clustering based on the 36-dimension feature vectors.</p>
        <p>As mentioned earlier the K-means [25] algorithm has proven to be the most efective for processing
smart meter data. It clusters data by partitioning it into k groups of equal variance, aiming to minimise
inertia criterion across clusters. K-means is both simple and eficient, scaling efectively with a large
number of samples and has been widely applied across various domains. In our study, K-means used
Euclidean distance between user profiles as the distance metric which can be expressed in terms of the
Euclidean norm of the diference between p and q vectors, or users in our case:</p>
        <p>To determine the optimal number of user clusters, it is important to evaluate using both inertia and
the Silhouette score, which are two widely used metrics for assessing clustering algorithms. Inertia [26],
also referred to as the within-cluster sum of squares, quantifies the compactness of clusters and decreases
as the number of clusters increases. Silhouette score [27] assesses how similar an object is to its cluster
compared to other clusters, taking into account both cohesion (similarity within the same cluster)
and separation (dissimilarity between diferent clusters). Silhouette scores range from -1 to 1, with
higher values indicating more well-defined clusters. Diferent numbers of clusters were tried in this
investigation, and the results are shown in the elbow plot in Figure 5.</p>
        <p>Balancing Inertia and Silhouette scores is crucial and Figure 5 suggests that using 5 or 6 clusters
is the best choice. Despite the Silhouette scores being similar for 5 and 6 clusters, choosing fewer
clusters is preferable, hence we chose 5 clusters. The centroid for each cluster was computed and users
with missing HDF data for certain months would be assigned to the appropriate cluster by adjusting
cluster centroids to match the lengths of available data for these users. This ensured accurate distance
calculations to determine the closest cluster for each case of missing data.</p>
      </sec>
      <sec id="sec-4-2">
        <title>4.2. Back-filling Energy Consumption Data</title>
        <p>Users with at least 12 months of smart meter data have annual bills estimated for each tarif and the
procedure for back-filling electricity consumption data for users with less than 12 months of data
involves several steps and leverages similarities in electricity consumption patterns from their closest
user cluster. This is shown in Figure 4. In step 1, users were matched to the closest cluster profile based
on only the number of months for which they have data. In step 2 the day, night, and peak consumption
ratios for the missing months were determined based on that closest cluster profile. Finally, in step 3,
the estimated monthly energy consumptions for each time slot in each month was back-filled using the
values from the cluster and normalised by the actual consumption figures for the months for which
there is data.</p>
      </sec>
      <sec id="sec-4-3">
        <title>4.3. Evaluation of Clustering Accuracy</title>
        <p>We assessed the accuracy of our approach to back-filling HDF data by performing an evaluation to
assess clustering accuracy, verify if cluster assignments aligned with the closest cluster profile, and
confirm the accuracy of back-filling for new users who submitted questionnaires after 15 th June 2024,
and who have more than 12 months of data.</p>
        <p>As indicated by the data duration analysis shown in Section 3.3, 78% of our users who uploaded their
HDF files were missing up to six months of usage data from within the past year so we reconstructed
where  is the forecasted value,  is the actual value, and  is the number of forecasts.</p>
        <p>SMAPE [28] is intended to measure the relative diference between predicted and actual values, taking
into account their magnitudes in a balanced way, where 0% signifies a perfect prediction. SMAPE can
efectively address the issue of having small or zero actual values in the denominator, which can lead to
a very high error percentage. It ofers a more balanced and robust measure as a result [ 28], compared to
Mean Absolute Percentage Error (MAPE). The SMAPEs for the three standard ToU periods are then
weighted based on their respective duration within the 24 hours —- 13 hours for day, 9 hours for night,
and 2 hours for peak —- resulting in an overall error value. The clustering was deemed accurate if the
assigned profile exhibited the best overall performance, as indicated by the lowest weighted SMAPE
value.</p>
        <p>When evaluating the feasibility of back-filling smart meter data for between one and six months, the
objective was to confirm that this extended period could produce reliable predictions, as indicated by
relatively low-weighted SMAPEs. This analysis would establish confidence in our back-filling process
and ensure the reliability of future forecasts.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Results</title>
      <sec id="sec-5-1">
        <title>5.1. Creation of User Profiles</title>
        <p>Five consumption clusters were identified based on a K-means analysis of te 36 features of the 24
users’ electricity usage patterns, all exhibiting a similar annual trend of increased usage in winter
and decreased in summer. We refer to the automatic clusters as profiles and across all profiles, users
demonstrate relatively low electricity usage during peak times. However, there are diferences in their
lifestyles and consumption behaviours between daytime and nighttime. The profile summaries are
shown in Figures 6 and 7.</p>
        <p>As shown in Figure 7, Profile 1, which we denote as the “day profile" , is the most prevalent, comprising
55% of households and predominantly consumes more electricity during daytime hours. In contrast,
Profiles 2, 3, and 4, collectively representing 36% of users, are categorised as “night profiles" where
households tend to use more energy during nighttime hours, especially during winter, possibly charging
an EV or availing of cheaper energy to run a heatpump. Finally, Profile 5, which accounts for 9%
of households, displays a relatively balanced electricity consumption pattern between day and night
but night usage outstrips day usage during the Winter months. These distinct consumption profiles
highlight a range of lifestyle and consumption habits among diferent households.</p>
      </sec>
      <sec id="sec-5-2">
        <title>5.2. Evaluation of HDF Data Back-Filling</title>
        <p>The sample users we used in this evaluation had submitted HDF files with full coverage of the
investigation period and as of July 2024, there were four such users (shown as A, B, C, and D in Table 4) who
met the criteria. Clustering results indicated that Users A and B were assigned to Profile 1 for each of
the six back-filling durations (back-filling for only the first month, then for the first two months, ...,
and finally for the first six months). User C was clustered into Profile 3 for back-filling of their first to
their first four months, and into Profile 4 for back-filling for five to six months. User D was assigned to
Profile 5 across all six back-filling months.</p>
        <p>The weighted SMAPE of estimated back-filling values vs. actual values are presented in Table 4. For
User A, when back-filled for one or two months, Profile 3 achieved the lowest SMAPE at approximately
15.3%. However, when back-filled for more than two months, Profile 1 consistently achieved a low
SMAPE, around 14.3%, suggesting it provides the best overall accuracy. The pattern for User B is more
pronounced, as the weighted SMAPEs for Profile 1 are consistently the smallest across all back-filling
durations. For User C, the SMAPEs are lowest in Profile 3 when back-filling for up to five months
whereas for the last back-fill duration, Profile 1 and Profile 3 have the same accuracy. The results from
these sample of users validate the clustering outcomes. However, for User D, Profiles 1 and 4 show lower
SMAPEs, which contrasts with our clustering which assigns User D to Profile 5. Further investigation
revealed that User D’s distances to the cluster centroids were very close across all profiles except Profile
2, suggesting that the user has a stochastic electricity usage pattern that does not align closely with any
of our extracted profiles.</p>
        <p>Overall, these findings validate the clustering outcomes, highlighting the reliability of our clustering
methodology in capturing stable load patterns. However, accurately predicting energy consumption at
the individual level may be less feasible for users exhibiting erratic load profiles and higher variability
as supported by previous research [29].</p>
        <p>For the stable users A, B, and C, the average weighted SMAPEs across six back-filling durations are
approximately 15.4%, 10.4%, and 19.3%, respectively. These weighted SMAPE values are less than 20%,
which is considered indicative of good forecasting performance [28]. This confirms that back-filling for
up to six months in our study is reliable despite the apparantly small amount of data used to create the
clusters, while maintaining reasonable prediction accuracy and highlights our confidence in accurately
estimating with six-month gaps in historical data.</p>
        <p>Substantial savings are available in domestic energy bills when a user chooses the most economical
tarif for them, which may be ToU or fixed-rate depending on the amount and the characteristics of their
use. It should be stressed that this analysis is based on usage patterns from profiles and that individual
users may find that their most economical tarif may be either a ToU or a fixed-rate one. For that, we
direct users to URL blocked to preserve double-blind submission but available in final version where they
can upload their own HDF data and where the analysis on their on data is performed directly and the
results sent to them.</p>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>6. Conclusions</title>
      <p>In this study, smart meter usage (HDF) data from more than one hundred users were gathered and
analysed to determine five typical consumption profiles. Due to data collection time and acquisition
channels, our sample size is relatively small compared to data gathered from national surveys. As the
smart meter installation program is still ongoing in Ireland and elsewhere, many households have had
them installed within the last year, leading to a limited duration usage data for such users.</p>
      <p>For users who do not yet have a full calendar year of their own historical HDF data, we developed
and evaluated a method to estimate and back-fill their usage to allow an estimation of their full annual
energy bill. This was done by categorising them into one of five consumption profiles and using the
usage patterns of the profile to complete the back-filling. The findings indicate that these estimates are
reliable when predicting based on up to six months of missing data. Households in Ireland can choose
from more than 60 tarifs from 10 suppliers but choosing the cheapest for each household can only be
done using their smart meter data which captures each household’s unique usage pattern. This work
allows users to use a full year of their own smart meter data to find their best energy tarif in a way
that accounts for seasonal factors, even if they have only 6 months of their own actual data.</p>
      <p>In summary, this study provides insights into an important area, namely estimating electricity
consumption with a view to understanding the economic advantages of choosing the best tarif plan. It
has the potential to benefit stakeholders by deepening customers’ understanding of their own energy
use and helping them to choose the cheapest tarif for them. Future work will explore the economic
impact of diferent tarifs from diferent energy suppliers in terms of their efects on consumer’s annual
bills.</p>
    </sec>
    <sec id="sec-7">
      <title>Acknowledgments</title>
      <p>This work was partly-supported by Research Ireland under Grant Number: SFI/12/RC/2289_P2,
cofunded by the European Regional Development Fund.</p>
    </sec>
  </body>
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