The diversity of residential electricity demand – A comparative analysis of metered and simulated data

Accepted Manuscript Title: The diversity of residential electricity demand - A comparative analysis of metered and simulated data Author: Jos´e Luis Ram´ırez-Mendiola Philipp Grunewald ¨ Nick Eyre PII: DOI: Reference:

S0378-7788(16)31398-6 http://dx.doi.org/doi:10.1016/j.enbuild.2017.06.006 ENB 7669

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Received date: Revised date: Accepted date:

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Please cite this article as: Jos´e Luis Ram´irez-Mendiola, Philipp Grddotunewald, Nick Eyre, The diversity of residential electricity demand - A comparative analysis of metered and simulated data, (2017), http://dx.doi.org/10.1016/j.enbuild.2017.06.006 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

The diversity of residential electricity demand - A comparative analysis of metered and simulated data Jos´e Luis Ram´ırez-Mendiolaa,∗, Philipp Gr¨ unewalda , Nick Eyrea a Environmental

Change Institute, University of Oxford,UK

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Abstract

A comparative study between simulated residential electricity demand data and metered data from the UK

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Household Electricity Survey is presented. For this study, a high resolution probabilistic model was used to test whether this increasingly widely used modelling approach provides an adequate representation of the statistical

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characteristics the most comprehensive dataset of metered electricity demand available in the UK. Both the empirical and simulated electricity consumption data have been analysed on an aggregated level, paying special

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attention to the mean daily load profiles, the distribution of households with respect to the total annual demands, and the distributions of the annual demands of particular appliances. A thorough comparison making use of both qualitative and quantitative methods was made between simulated datasets and it’s metered counterparts.

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Significant discrepancies were found in the distribution of households with respect to both overall electricity consumption and consumption of individual appliances. Parametric estimates of the distributions of metered

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data were obtained, and the analytic expressions for both the density function and cumulative distribution are given. These can be incorporated into new and existent modelling frameworks, as well as used as tools for further analysis.

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Keywords: Domestic electricity use, Energy demand modelling, Electricity demand load profiles

∗ Corresponding

author: Email address: [email protected] (Jos´ e Luis Ram´ırez-Mendiola )

Preprint submitted to Energy and Buildings

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1. Introduction

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progresses, robust modelling tools become even more

42

relevant. The effectiveness of low-carbon measures

It is a well known fact that the residential sec-

43

such as the implementation of Demand-Side Man-

3

tor is a major contributor to overall electricity con-

44

agement (DSM) strategies relies heavily on the ex-

4

sumption in most countries. Residential electricity

45

tent to which we understand residential electricity

5

consumption in the UK accounts for over a third of

46

consumption. A better understanding of the electric-

6

the national total [5]. Moreover,it is also well known

47

ity consumption patterns, and the potential changes

7

that the domestic sector contributes significantly to

48

these may undergo, would allow us to devise the most

8

peak demand, especially during winter. Over the

49

suitable measures.

9

last decade, however, the potential of this sector to

50

As new, relevant data become available, opportu-

10

contribute towards reductions in energy consumption

51

nities for further improvement in our models arise.

11

and CO2 emissions has been increasingly recognised.

52

The lack of information about consumer behaviour

12

This, in turn, has sparked the interest in this research

53

and appliance usage during the development of mod-

13

area.

54

els such as the one used in this study (see Section 3)

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In particular, there is an increasing interest in un-

55

may lead to problems which could not have been re-

15

derstanding the consumption patterns of the resi-

56

vealed with the data available at the time. However,

16

dential sector, and how these might change in re-

57

17

sponse to changes in climate and energy prices, and

58

18

the implementation of new supply-demand balancing

59

19

strategies and other low-carbon measures.

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sources of data currently available provide us with an opportunity to re-assess the models’ performance.

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by applying these models in a different context to the one in which they were validated, these issues can

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now be revealed and explored. Moreover, the new

To this end, several efforts have been made to

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model electricity demand, seeking to quantify the

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In particular, it is worth verifying that the simulated

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energy requirements at different levels of analysis.

63

electricity consumption data produced by the mod-

23

Two fundamentally different approaches divide these

64

els aggregate such that the statistical characteristics

24

modelling efforts: top-down and bottom-up. This

65

observed in the metered data are well represented,

25

terminology refers to the hierarchical level of the

66

as this is key to a robust bottom-up model.

26

data inputs. Top-down models focus on describing

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In the following section brief descriptions of the

27

the overall trends observed in historical records, with

68

evolution of residential energy demand modelling

28

little or no interest in individual end-uses. In con-

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and the state of the art are given. The next two

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trast, bottom-up models focus on representing the

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sections concern a description of the key elements

30

contribution of each end-use towards the aggregate

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of the analysis presented, namely the probabilistic

31

consumption and overall trend. A more detailed de-

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demand model used and the sub-metered electricity

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scription of these two approaches can be found in

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consumption data. The methodology for the com-

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[19].

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parative analysis, which encompasses both qualita-

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Electricity demand modelling has proved very im-

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tive and quantitative methods, is discussed in Sec.

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portant in both academia and industry. In particu-

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5.1. This is followed by a discussion of the analy-

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lar, bottom-up models’ ability to incorporate many

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sis results, where the critical shortcomings identified

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different factors into the modelling has been key to

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are highlighted. Finally, a summary of concluding

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identifying and understanding the essential elements

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remarks based on the results previously described is

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associated with the production of demand loads. As

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given, as well as further details about potential di-

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the transition towards low-carbon energy systems

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rections of future work.

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2. Residential electricity demand modelling

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ability to represent the diversity of energy demand

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across time and populations.

In terms of demand for electricity, the variability

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The model developed by Yao and Steemers [26]

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across households is high. In the UK, for instance,

125

is a good example of a deterministic model. The

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according to data from the Office of Gas and Electric-

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simulation of demand loads is based on fixed, pre-

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ity Markets (Ofgem), ‘Typical Domestic Consump-

127

determined household activity patterns characterised

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tion Values’ for electricity range from 2000 to 7200

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mainly by the periods of absence. Appliances are al-

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kWh/year [13].

The results of the most detailed

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located based on national ownership statistics. Their

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study (to date) of electricity use in English house-

130

associated demand is calculated based on average

90

holds would appear to indicate that there is an even

131

ratings and frequency of use estimates. The model is

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higher variability, with values ranging from 560 to

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able to produce rough estimates of half-hourly daily

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14580 kWh/year [16].

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load profiles. Another example of a deterministic model is presented in [23].

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There are many factors associated with this vari-

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ability. The variations in energy consumption associ-

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Recognising the limitations of the deterministic

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ated with differences in dwelling characteristics and

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approach, several attempts to capture the variability

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the impact of ambient temperature/climate condi-

137

observed in real households were made. An emerg-

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tions have have been extensively studier. However,

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the impacts of the differences in dwellings’ appliance

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content, and the usage patterns of such appliances

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have not been studied as much.

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patterns. These, in turn, are used in the development of probabilistic models. Page et al. [15] devel-

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ing approach, which continues to attract interest, is based on the use of data from Time-Use Surveys (TUS) for the extraction of characteristic activity

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Accounting for the impact different combinations

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of these factors have is critical in representing the

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oped a general methodology for the use of Markov

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range of consumptions currently observed. Conse-

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chain modelling techniques for the simulation of ac-

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quently, the bottom-up approach to demand mod-

145

tivity sequences. Several variations of this method-

105

elling has been favoured for this purpose. Method-

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ology, supported by the use of country-specific TUS

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ologies that follow this approach offer the advantage

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data were implemented.

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of modelling demand with greater level of detail. De-

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monly cited examples are the models developed by

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mand estimates can be calculated at the household

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Wid´en and W¨ackelg˚ ard [24] and Richardson et al.

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or even end-use level.

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[18], which are based on Swedish and UK data, re-

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ed

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Some of the most com-

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A branch of bottom-up modelling is characterised

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spectively. The reader is referred to [20] for a more

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by a focus on user activity-based simulations of de-

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comprehensive review of models based on this ap-

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mand patterns. Models falling within this group can

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proach.

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be further divided into deterministic and probabilis-

154

A few attempts at improving this widely adopted

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tic models. Deterministic models are based on as-

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modelling approach have been made. These, how-

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sumptions about seemingly direct causal links be-

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ever, have focused on the refinement of the simu-

116

tween chosen drivers and expected outcomes.

In

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lation of occupancy profiles. To this end, different

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contrast, probabilistic models make use of stochastic

158

methods have been applied.

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methods for the simulation of electricity consump-

159

One of these approaches has focused on improv-

119

tion patterns. This kind of models make predictions

160

ing the representation of the duration of the occu-

120

about different outcomes based on the stochasticity

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pancy states through the use of semi-Markov models.

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of the input data. These models have, therefore, the

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In the model presented in [25] the transition prob-

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abilities are based on the French TUS, and Weibull

204

of country-specific TUS data and statistics on appli-

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distributions are used to model the duration of the

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ance ownership and average ratings. Despite these

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occupancy states. In the model presented in [1] the

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differences, the approach to converting activity pat-

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transition probabilities are based on the Belgian TUS

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terns into electricity demand loads has remained es-

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and non-parametric estimates are used to model the

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sentially the same. Therefore, although this model is

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duration of the occupancy states.

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based on UK-specific data, the results of the analy-

Another approach has focused on the identifica-

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sis presented in this paper are relevant to any model

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tion of characteristic activity patterns which exhibit

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using a similar approach. In the following section,

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statistically significant differences. In the model pre-

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a more detailed description of the CREST model is

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sented in [4] a Bayesian clustering technique is used

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presented.

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for the identification of household-level activity pro-

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files. In the model presented in [1], a hierarchical

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3. The CREST model

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agglomerative clustering approach is used for iden-

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tifying characteristic individual occupancy patterns.

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In both models, the clustering approach is comple-

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mented by the development of a Markov model for

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the identified clusters.

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demand was developed at CREST (Centre for Re-

217

newable Energy Systems Technology, Loughborough

218

University). This is a probabilistic model that pro-

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model developed by Richardson et al. [18]. In addi-

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tion to the extension of the model to include ther-

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mal demand loads, the simulation of occupancy se-

vides an estimate of the electricity consumption of individual households based on the number of res-

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The model presented in [10] is an extension of the

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In 2010 a new model for residential electricity

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219 180

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quences was refined. The original model was based

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on two-state occupancy patterns simulations. The

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refined version is based on the simulation of four-

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state occupancy patterns. Both models, however,

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make use of the first-order Markov chain technique

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for the production of the occupancy sequences. The

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electricity demand model was left largely unaltered.

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The only modification being the removal of end-uses

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associated with thermal demand loads. This original

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model for electricity demand has found widespread

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applications in academia and industry, for instance

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[6, 11, 3, 2, 8].

idents, occupancy patterns and dwelling appliance

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content. Based on the approach developed by Page

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et al. [15] for the implementation of Markov chain

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221

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models based on time-use data, Richardson et al. de-

225

veloped a residential building occupancy model [17].

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Later on, this occupancy model was combined with

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the approach developed by Yao and Steemers [26]

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for generating switch-on events of electric appliances

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to create a new probabilistic model that has found

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widespread application in the literature [18]. The

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model is capable of generating electricity load pro-

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files of individual households as derived from the sim-

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ulated use of individual appliances.

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3.1. Structure

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The structure of the model developed by Richard-

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The model is divided into two modules. The first

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son et al. [18], also known as the CREST model,

236

one is responsible for the simulation of dwelling oc-

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shows great similarity to that of other, more re-

237

cupancy patterns.

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cent models.

There are, however, differences be-

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for the conversion of the simulated activity patterns

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tween some of the key elements of the structure.

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into electricity demand loads. Occupancy profiles

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The main difference concerns the approach to simu-

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are simulated for each household, for each day of the

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lating occupancy patterns, as discussed in the para-

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simulated period. These profiles are based upon data

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graphs above. A lesser difference concerns the use

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from the UK 2000 Time-Use survey [9]. The data

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The second one is responsible

Page 4 of 21

from this survey is representative of national time

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average). For the simulations used in the original

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budgets [12]. The version of the model used for the

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validation analysis this value was set between 4100

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simulations described in this paper features a two-

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and 4300 kWh; this in order to represent dwellings

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state occupancy model. Individual occupancy pro-

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from a specific region in the UK. The calibration of

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files are essentially binary sequences of states corre-

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the model is meant to ensure that the overall average

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sponding to periods of active and inactive occupancy.

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annual consumption of the simulated set of house-

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The active occupancy states also take account of the

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holds is around a particular value, which is one of

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number of household members currently active.

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the input parameters for the model.

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3.2. Validation

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Each simulated household is allocated a particular

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set of appliances. Appliances are taken from a pre-

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defined set of 33 common appliances and randomly

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For the purpose of validating the CREST model,

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allocated based on national ownership statistics. The

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household-level electricity consumption data was me-

255

simulated appliances are configured using statistics

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tered from 22 households in the East Midlands [18].

256

that include their mean total annual electricity con-

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The households’ electricity consumption was moni-

257

sumption, average power rating, and average cycle

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tored for a full year. Thus, the resulting metered

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length. This configuration is meant to ensure that

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dataset contained around eight thousand 1 min res-

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the appliances represent some general behaviour or

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pattern rather than emulate some specific real-life

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appliance (a specific make, or any other specific char-

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acteristics). In this sense, CREST’s ‘appliances’ are

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itored households. The simulations runs covered the

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rather categories of sorts into which many real-life

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equivalent of a full year period, and generated data

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appliances are expected to fit.

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olution daily load profiles. The model was then calibrated against the collected data, and used for simu-

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lating the electricity consumption from the 22 mon-

with the same resolution as the metered data.

The activation of some of these ‘appliances’ dur-

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The simulation output was compared against the

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ing the simulations depends on the presence of active

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original metered data. The validation analysis was

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occupants in the dwelling. Therefore, the variation

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based on comparisons of different aspects, including

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in appliance usage is based upon the activity of the

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the variation of annual demand between dwellings.

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members of the household and their number. A de-

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One of the aims was to formally assess the extent

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mand load profile is generated for each allocated ap-

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to which these datasets differ from one another in

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pliance for each day of the simulated period. The

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terms of this variation. To this end, a statistical

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loads generated depend on the occupancy profiles

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significance test, namely the Mann-Whitney U test,

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previously generated. The total daily load profile is

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was used [18]. The purpose of this test is to de-

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the result of aggregating all of the appliances’ daily

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termine how likely it is that the simulated dataset

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demand loads.

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corresponds to a sample drawn from the same pop-

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The variation in electricity consumption between

316

ulation as the reference sample (metered dataset).

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different households is achieved through changes in

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One of the advantages of this test is that it can be

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the household composition, set of appliances, and oc-

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applied even when the distributions of the data are

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cupancy patterns of each simulated dwelling. More-

319

not known. The resulting measured and simulated

280

over, a calibration factor provides a means to align

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annual consumptions are shown below in Fig 1(A).

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the overall average household consumption of the

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In summary, the comparison between metered and

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simulated sample to the relevant average annual con-

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simulated datasets appeared to show that there was

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sumption (e.g. sample group, regional or national

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no significant statistical difference between them,

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Page 5 of 21

thus validating the model. The CREST model is

362

day of the monitoring period. For some households

325

a good example of the attempts to link activity pro-

363

total demand load, as read from the mains, was

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files to electricity consumption via the simulation of

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also recorded. The overall length of the monitoring

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appliance usage. For this reason, we were particu-

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period varies across households. 26 of them were

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larly interested in looking at how well represented

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monitored for a full year. The rest were monitored

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is this link by the simulations when compared with

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for “one-month-long” periods with effective lengths

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a larger, highly disaggregated metered dataset. A

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varying between 20 to 30 days, and covering different

331

more detailed description of the data used for this

369

parts of the trial period.

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purpose is given below in Sec. 4.

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The resolution of the metered electricity consump-

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tion profiles also varies. For households monitored

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for a full year, electricity consumption was metered

4. The UK Household Electricity Survey

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every 10 min. For the rest of the households, it

the result of a study jointly commissioned by Defra,

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was metered every 2 min. The resulting dataset is

DECC and the Energy Saving Trust [7]. The study

375

336

a collection of highly detailed electricity consump-

had four main objectives:

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337

tion profiles, which already has provided very im-

377

portant insights into the way electricity is used in

• To identify the range and quantity of electrical 378

appliances found in the typical home.

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• To understand their patterns of use and their impact on peak electricity demand.

341

• To monitor total electricity consumption of the

343

homes as well as that of individual major appli-

344

ances in the household.

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• To collect user habit data when using the range

exhausted. Further analysis would allow us to have a better understanding of some of the issues associ-

382

ated with residential electricity consumption, such as

383

the scope for demand shifting, estimation of stand-by

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consumption, the effects of changes in the size and

385

efficiency of appliances, and differences in the way

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different socio-economic groups use electricity.

of appliances present in the households.

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nities for exploiting such a rich source are far from

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ed

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the UK’s residential sector. However, the opportu-

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The UK’s Household Electricity Survey (HES) was

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The characteristics of this dataset make it ideal for

For this study 250 owner-occupier households were

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testing current approaches to modelling of residen-

348

monitored over the period May 2010 to July 2011.

389

tial electricity use. In particular, we are interested

349

The final report on this study observes that the mon-

390

in testing whether a model such as CREST could

350

itored households were chosen such that the statisti-

391

provide us with simulated data that adequately rep-

351

cal characteristics of the sample would match closely

392

resents the statistical characteristics observed in HES

352

those of the typical socio-economic mix [27]. Only

393

data.

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owner-occupiers were recruited for the study. The

354

households, however, were still fairly typical in terms

394

5. Comparison of CREST model’s simula-

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of socio-demographic factors. The average annual

356

electricity consumption across the sample was 4093

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kWh/year, which compares very well to the 4115

396

The information about the relationship between

358

kWh/year average (as of 2015) across all UK homes

397

consumer behaviour and appliance usage was more

359

[5].

398

limited at the time models such as CREST’s were

was

399

developed. The issues caused by such lack of in-

recorded for each of the 250 households for each

400

formation could not be revealed using the metered

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Appliance-level

electricity

consumption

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tions against HES data

Page 6 of 21

electricity consumption data available at the time.

440

final sample resulting from excluding 6+ member

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However, the arrival of richer datasets allows us to

441

households consisted of a total of 243 households,

403

explore these issues now by applying these models in

442

of which 24 had annual records. We will refer to this

404

a different context to the one in which they were val-

443

dataset as HES243. The extent to which this filtering

405

idated. Now that more comprehensive datasets are

444

affects the analysis will be discussed in Sec. 7.

406

available, such as the one provided by HES, this pa-

445

In order to test the simulation outputs against

407

per re-assesses CREST model’s assumptions on ap-

446

the whole HES dataset, the comparative analysis

408

pliance usage and their corresponding impacts on

447

between simulated and metered data was divided

409

daily electricity load profiles and the variability of

448

into two parts. Firstly, we focused on the 24 HES

410

annual consumption across households.

449

households that were monitored for a full year. The

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The interest in testing this model against the HES

450

corresponding dataset will be referred to as HES24

412

data resides in great measure in the fact that the

451

throughout the rest of the paper. The existence of

413

group of monitored households is much more diverse

452

this sub-set of households with annual records proves

414

than any previous group. Moreover, the appliance-

453

important, as it gives us the opportunity to make a

415

level electricity consumption profiles provide us with

454

closer comparison between the results of the analysis

416

a further point of comparison between simulated and

455

of this HES24 sub-set and the set of 22 households

417

metered data.

456

5.1. Methodology

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used for the original model validation (See Sec. 3.2). We will refer to the latter dataset as CREST22. Secondly, we then extended the analysis to the

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an

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We wanted to reproduce, to some extent, the orig-

459

rest of the HES sample so as to be able to assess

420

inal model validation. For the original validation a

460

the model’s ability to represent the statistical char-

421

relatively small sample consisting of 22 households

461

acteristics observed in a larger, more comprehensive

422

was used (see Sec. 3.2). Total daily demand for

462

metered dataset. However, the sub-set of 219 house-

423

electricity was monitored for a full year. These me-

463

holds for which only monthly records were present

424

tered data allowed for comparisons of total annual

464

had to be processed in a different way to the set of

425

demands and aggregated load profiles between me-

465

households with full year records.

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tered and simulated households. In contrast, HES

466

Total household annual consumptions are not ex-

427

data offers the opportunity to compare total an-

467

plicitly included in the HES data. This informa-

428

nual consumption levels, individual appliances’ an-

468

tion had to be extracted from the records available

429

nual consumption and aggregated load profiles of a

469

for each household. Most households had monthly

430

group of households over 10 times larger.

470

records only, so these had to be used for producing

471

an estimate of the household’s total annual consump-

472

tion. For each household with monthly records only

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5.1.1. Data processing

432

Preliminary analysis of HES data revealed that

473

the available data was used for calculating total daily

433

some of the households monitored during the study

474

consumptions for each day in the monitoring period.

434

are composed of 6+ members. Based on its present

475

Then, based on the distribution of total daily con-

435

configuration, the CREST model can only simulate

476

sumptions, the total daily consumptions for the miss-

436

households of up to 5 members. For this reason and

477

ing days needed to complete a full year were gener-

437

the sake of consistency, the original HES sample was

478

ated stochastically to add some variation. The gener-

438

“filtered” so as to be able to make a direct compar-

479

ated daily consumptions were then grouped into the

439

ison between metered and simulated samples. The

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months corresponding to the same monitoring period

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Page 7 of 21

as that of households with annual records, and the

522

tions compare to those of the corresponding metered

482

corresponding monthly seasonal factor was applied.

523

appliances. To this end, we also extracted the total

483

Finally, all daily loads were added up thus provid-

524

annual consumptions of individual appliances for the

484

ing an estimate of the total annual consumption of

525

households in the HES243 dataset.

485

that particular household. The case of the 24 house-

526

As observed in Section 3.1, the CREST model gen-

486

holds with annual records was more straightforward

527

erates artificial electricity consumption data based

487

as we only had to add up the consumptions recorded

528

on the simulation of appliance usage for a pre-defined

488

throughout the year. In addition to the total annual

529

set of appliances. Among the model’s pre-defined

489

consumption, a mean daily load profile for the whole

530

set, there are ‘appliances’ which are meant to rep-

490

HES sample was calculated based on all available

531

resent the consumption of the appliances listed in

491

data.

532

Table 1. This pre-defined set includes some other

cr

ip t

481

For the simulation of electricity consumption data

533

‘appliances’ which represent the electricity consump-

493

the CREST model was used. A full version of the

534

tion of some other devices with more predictable con-

494

CREST model is publicly available in the form of

535

sumption patterns (e.g. cold appliances). However,

495

an Excel spreadsheet model (See [18]). However, for

536

we focus the analysis on the appliances listed in Ta-

496

the purpose of simulating the electricity consump-

537

ble 1, as the electricity loads generated by the use

497

tion of the same number of households as in the HES

538

498

sample, the CREST model was re-implemented in

539

499

Python in order to allow for faster, multiple auto-

540

500

mated runs. Features, functionality and results of

541

501

Python and Excel versions of the model are equiva-

542

502

lent. We used this Python implementation for gen-

543

on the activities they are associated with: cooking,

503

erating a year’s worth of artificial electricity con-

544

washing, TV watching, and ICT related activities.

504

sumption data for 243 households. Each simulated

545

Both CREST and HES appliances are grouped in

505

household profile was matched to a metered counter-

546

these more general categories, as shown in Table 1.

506

part in the HES243 dataset. Since it is possible to

547

In most cases it is possible to make a one-to-one com-

507

specify both the day and the month when running

548

parison between HES and CREST appliances in spite

508

simulations, the simulated period was also matched

549

of the differences that may exist between them.

509

to the monitoring period of the corresponding me-

550

In order to obtain the distributions of the simu-

510

tered households. Total annual consumptions corre-

551

lated total annual consumption of individual appli-

511

sponding to each household were calculated, as well

552

ances, it was necessary to run a new set of simu-

512

as the mean daily load profile for the whole simu-

553

lations. Based on the original model configuration,

513

lated HES243 sample. For the first part of the analy-

554

appliances are allocated to the simulated households

514

sis, which focused on the HES24 dataset, simulations

555

on a random basis. Therefore, the original model

515

were run based on the specifications of this sub-set

556

implementation had to be modified so as to ensure

516

of households only.

557

that the appliances of interest were allocated to the

an

us

492

of these appliances are the ones with direct links to households’ activities. We compare the simulated

Ac ce

pt

ed

M

demand of these appliances with the data from their corresponding metered counterparts. The appliances of interest were grouped based

517

As the electricity consumption of individual appli-

558

relevant households. The goal was to match the ap-

518

ances is available from both metered and simulated

559

pliance configuration of the simulated households to

519

data, there was an interest in looking at how the es-

560

that of the metered counterparts.

520

timates of the annual consumptions of the simulated

561

HES records show which appliances are owned by

521

appliances are distributed and how these distribu-

562

which households. Based on this information, house-

8

Page 8 of 21

holds were grouped accordingly. Using the modified

586

is not simply a smoothing method. This method of-

564

model implementation, simulation runs correspond-

587

fers a way of obtaining an accurate non-parametric

565

ing to one year long periods were carried out.

588

estimate of the PDF of a given dataset. This esti-

589

mate is in fact the best possible estimate of the dis-

590

tribution of the original population from which the

591

sample was drawn. It can be shown that the kernel

592

density estimate converges to the real distribution as

593

the sample size increases, and it’s convergence rate

594

is the highest among all estimates [22].

hob, oven, microwave, kettle

Washing

Washing machine, Tumble dryer, Dish washer

Washing machine, washer dryer, Tumble dryer, Dish washer

TV1, TV2, TV3

TV1, TV2, TV3, CRT TV, LCD TV, plasma TV, Audio-visual site

PC

Desktop PC 1, Desktop PC 2, Computer site, Laptop 1, Laptop 2

TV watching ICT related

595

As observed above, some statistical significance

596

tests are based on the properties of ECDFs. This

597

leads naturally to the quantitative part of this com-

598

parative analysis, which focuses on the use of such

599

tests. For the quantitative comparison we will use

600

two tests, namely, the Kolmogorov-Smirnov test and

601

the Mann-Whitney U test.

602

566

603

5.1.2. Comparative analysis

Both tests are non-

parametric, which means they do not make assumptions about the distribution of the data. Both tests can be used to compare two unpaired datasets, both

M

604

cr

Cooking

cooker1, cooker2, hob1, hob2, oven1, oven2, hob+oven, microwave1, microwave2, kettle1, kettle2

us

Appliances contained CREST HES

Categories

an

Table 1: Categories of appliances and the appliances contained in each one, according to the appliances present in both metered and simulated datasets.

ip t

563

In order to assess whether the simulated data is

568

consistent with the metered one, both qualitative

569

and quantitative methods were used.

605

focus on comparing the statistical characteristics of

606

the distributions of the two datasets being compared,

607

and both are robust to the presence of outliers. How-

608

ever, the two tests work in a very different way.

ed

567

570

The qualitative comparison between datasets fo-

571

cused on the Empirical Cumulative Distribution

572

Function (ECDF) of the different datasets.

573

ECDF is a formal direct estimate of the Cumulative

574

Distribution Function1 from which simple statisti-

575

cal properties can be derived. Moreover, the ECDF

576

properties form the basis of various statistical signi-

577

ficance tests.

pt

Ac ce

578

The Probability Density Function (PDF) of the to-

579

tal annual consumptions was obtained as well, as it

580

provides a better graphical representation of some of

581

the statistical characteristics of the metered HES243

582

dataset. In order to obtain a reliable representation

583

of the PDFs, the Kernel Density Estimation (KDE)

584

method was used. Kernel Density estimation is often

585

used as a data smoothing technique. However, KDE 1 Cumulative

609

The Kolmogorov-Smirnov (KS) test compares the

610

cumulative distribution of the two data sets in ques-

611

tion, and calculates a p-value that depends on the

612

largest difference between the two distributions. The

613

test is sensitive to any differences in the two distri-

614

butions. Significant differences in shape, spread or

615

median values will result in a small p-value. The KS

616

test can also be used to test whether an empirical

617

distribution is consistent with an ideal distribution,

618

and therefore, it is commonly used as a test of good-

619

ness of fit, or for testing for normality. In essence,

620

this test answers the question: If the two samples

621

were randomly drawn from different parent popula-

622

tions, how likely it is that the two parent populations

623

have the same statistical distribution?

The

distribution function (CDF) - It is a function whose value is the probability that a corresponding continuous random variable has a value less than or equal to the argument of the function.

624

The Mann-Whitney (MW) test compares two

625

datasets by ranking the elements in the dataset from

626

smallest to largest, and calculating the average of

9

Page 9 of 21

the rank scores of the elements in the two datasets.

663

6. Analysis results

628

A p-value is calculated which depends on the differ-

629

ence between the average ranks of the two datasets.

664

6.1. Variations in annual demand levels

630

Compared to the KS test, the MW test is mostly

665

The high variability observed in annual demand

631

sensitive to changes in the median value. The MW

666

levels across the monitored households clearly re-

632

test is closely related to the t-test. However, the MW

667

flects the fact that different households mean differ-

633

test is more widely applicable than other more pop-

668

ent needs, lifestyles and consumption patterns. In

634

ular tests such as the t-test, as it does not require

669

this context, when we talk about variability, we re-

635

the assumption of normally distributed data, and it

670

fer to the natural variation that is observed in the

636

is much more robust to the presence of outliers. In

671

demand levels as a result of the differences in the

637

essence, the MW test answers the question: If both

672

underlying causes of said demand.

638

samples come from the same population, how likely

673

Fig. 1 shows both simulated and metered annual

639

it is that random sampling would result in the dif-

674

demands, obtained from the different datasets. Both

640

ferences observed in this particular case?

675

the variability of annual demand among households

676

and the differences between the metered and simu-

677

lated levels can be appreciated, as well as how they

As we are interested in determining whether the

642

simulated data generated by the model accurately

643

capture the statistical characteristics of the metered

644

data, we use these test to obtain a quantitative mea-

645

sure of how closely related the two datasets are. In

646

other words, we use these tests to assess whether

647

both datasets are consistent enough with statistical

648

samples drawn from the same population, or whether

649

the two datasets are consistent with samples drawn

650

from populations which follow the same statistical

651

distribution. The MW test provides us with a quan-

652

titative measure of how likely the former situation is,

653

whereas the KS test provides us with a measure of

654

how likely it is the latter.

679

cr

us

compare across datasets. This figure starts to show that the empirical data has greater diversity than the model simulations would suggest. The red horizontal

M

680

an

678 641

ip t

627

681

lines indicate the overall average annual consumption

682

of the corresponding metered dataset. Only one line per section is needed because, as observed in section

684

3, an adequate calibration of the CREST model en-

685

sures that the overall average annual consumption

686

of the simulated sample is around a specified value.

687

The corresponding values are listed in Table 2 which

688

shows, in numbers, how the variability of both simu-

689

lated and metered data compares across the different

690

datasets.

Ac ce

pt

ed

683

691

The mean annual electricity demands per dwelling

692

calculated from metered and simulated data for each

693

of the analysed datasets differ by around 1%. The

694

fact that this difference is small only shows that the

655

The MW test was also used in the original val-

695

model was appropriately calibrated. Despite this, it

656

idation of the CREST model (see Sec. 3.2). The

696

is observed that the differences in standard devia-

657

positive results of the test were one of the arguments

697

tions are considerably larger. For both HES24 and

658

in favour of the validation of the model. We take this

698

HES243 datasets the standard deviation of the me-

659

as an opportunity to show the effect that sample size

699

tered annual consumptions is about 40% higher than

660

may have when using this kind of test by applying

700

the standard deviation of the simulated ones.

661

the test to the datasets HES24 and HES243 sepa-

701

The results of the first part of the analysis, con-

662

rately and comparing the results.

702

cerning the HES24 dataset, already appeared to sug-

10

Page 10 of 21

gest that the variation in annual demand levels was

709

the standard deviation of the metered annual con-

704

being under-represented.

However, the simulated

710

sumptions was about 30% higher than the standard

705

HES24 dataset used for this study appears to be con-

711

deviation of the simulated ones. Despite this seem-

706

sistent with the simulated CREST22 dataset used in

712

ingly large difference, the result of applying a statis-

713

tical significance test would appear to indicate that

714

the datasets were not significantly different (See Sec.

715

3.2).

716

6.2. Empirical cumulative distributions and signifi-

707

2

the original validation analysis (See Table 2).

cance tests

717

ip t

703

The HES24 dataset is very similar in size to

719

the CREST22 dataset used for the original valida-

720

tion. As part of the original validation analysis, a

721

Mann-Whitney (MW) test with a 5% level of signi-

722

ficance was used to compare metered and simulated

723

CREST22 datasets. Based on the test results, it was

725

us

concluded that there was no significant difference between them (Sec. 3.2). In addition to verifying this, and in order to further test how well represented was

M

726

an

724

cr

718

727

the metered data by the simulations in the original

728

analysis, we extracted the annual consumption data from the original validation results and performed

730

a Kolmogorov-Smirnov (KS) test on these datasets.

731

The results of this test also supported the hypothesis

732

that the two datasets are consistent with each other.

733

The same tests were then applied to metered and

734

simulated HES24 datasets. With a p-value of 0.38,

735

the MW test with 5% significance level suggests that

736

it is likely that these two samples were drawn from

737

the same population. Moreover, with a p-value of

738

0.44, the KS test with 5% significance level suggests

739

that it is likely that these two samples come from

740

populations equally distributed. The results of this

741

part of the analysis seem to be well in agreement

742

with those of the original validation, thus confirming

743

that the model produces reasonable estimates when

744

dealing with small samples (∼ 20 households).

pt

ed

729

Ac ce

Figure 1: Annual electricity demands by household, ranked by magnitude: A) Annual demands of both metered and simulated households in CREST22 dataset (adapted from Ref. [18, Fig. 6]). B) Annual demands of both metered and simulated households in HES24 dataset. C) Annual demands of both metered and simulated households in HES243 dataset. Households were grouped in sets of five. The levels observed correspond to the average consumption of each set.

Table 2: Mean values and standard deviations of annual electricity consumptions datasets. CREST22

708

HES24

HES243

metered

simulated

metered

simulated

metered

simulated

Mean annual demand (kWh/y)

4172

4124

4624.6

4629.7

3944.5

3942.9

Standard Deviation (kWh/y)

1943

1372

2510

1545

2348

1405

Coefficient of variation

0.47

0.33

0.54

0.33

0.60

0.36

The analysis of CREST22 datasets showed that 2 CREST22

data was taken from [18])

745

The second part of the analysis, which focused

746

on the HES243 datasets, was aimed at determining

747

whether the model simulations produce a reasonable

748

representation of the statistical characteristics of a

11

Page 11 of 21

larger, more diverse set of households. Both MW

772

ciated in Fig. 2. The Kernel Density Estimate of

750

and KS test were used again to provide a quanti-

773

the distribution of metered annual consumptions re-

751

tative measure of the differences between metered

774

vealed the existence of a more complex underlying

752

and simulated datasets. On this occasion, however,

775

distribution. Based on this estimate, three clusters

753

the tests results revealed the existence of important

776

can be readily identified. What this shows is that the

754

differences in the statistical characteristics of both

777

distribution of households with respect to total an-

755

datasets.

With a p-value of 0.049, the MW test

778

nual consumption is concentrated in three clusters,

756

with 5% significance level now suggests that it is un-

779

centred around the values (modes): 1.58 MWh, 3.92

757

likely that the metered and simulated HES243 sam-

780

MWh and 7.85 MWh. Based on this information,

758

ples come from the same population. In a similar

781

and on the same principles behind the Kernel Den-

759

manner, with a p-value of 0.001, the KS test with

782

sity Estimation, we produced a parametric estimate

760

5% significance level suggests that it is very unlikely

783

for the empirical PDF observed in Fig. 2. This es-

761

that these two samples come from populations with

784

timate can be expressed by the following trimodal

762

the same statistical distribution. Moreover, by us-

785

Gaussian mixture:

763

ing the KS test to test for normality, we found that

764

the simulated HES243 dataset appears to be consis-

765

tent with normally distributed data (p-value of 0.81).

766

The metered HES243 sample is not. These results

767

are best appreciated graphically. As Fig. 2 shows,

768

the simulated HES243 dataset is well in agreement

786

where Ni (x | µi , σi ) =

769

with its corresponding normal fit (dashed line).

787

eral normal distribution with mean µi and standard

788

deviation σi , and Ci is a proportionality constant.

us

cr

ip t

749

Ac ce

pt

ed

M

an

f (x) ∼ C1 N1 (x | µ1 , σ1 ) + C2 N2 (x | µ2 , σ2 )

(1)

σi

1 √

e 2π

− 21



x−µi σi

2

is the gen-

789

A summary of the parameters of this estimate and

790

their corresponding values can be found in Table 3.

791

Fig. 3(A) shows how this trimodal Gaussian model

792

compares to the empirical PDF.

793

The ability to produce a parametric estimate for

794

the PDF means that it is also possible to find an ex-

795

pression (F (x)) for the CDF, as these two functions

796

797

798

Figure 2: Distribution of total annual consumptions: A) Probability Density Functions of metered and simulated HES243 datasets. B) Empirical Cumulative Distribution of metered and simulated data. The dotted lines around the ECDF of the metered HES243 dataset are the 95% confidence bounds.

+C3 N3 (x | µ3 , σ3 )

are related analytically by the equation: F (x) = Rx f (t)dt. Therefore, by integrating f (x) we ob−∞ tain that the CDF is given by:

   3 X Ci x − µi √ F (x) = 1 + erf 2 σi 2 i=1

(2)

799

where erf(x) is the error function, and Ci , µi and σi

800

are the same parameters used in equation (1) (see

770

Probability density functions corresponding to

801

Table 3). The way this estimate compares to the

771

each set of annual consumptions can also be appre-

802

ECDF is shown in Fig. 3(B).

12

Page 12 of 21

tion falls within the interquartile range of the cluster

821

in question. Households in each cluster were further

822

grouped according to size. The percentage composi-

823

tion of each cluster is shown in Fig. 4(B).

us

cr

ip t

820

N2 (µ2 , σ2 ) 0.622 3.92 1.28

N3 (µ3 , σ3 ) 0.115 7.85 1.0

ed

Ci µi σi

N1 (µ1 , σ1 ) 0.261 1.575 0.78

Figure 4: Distribution of households according to size and annual consumption range: A) EPDFs corresponding to households grouped by size. The vertical line in each distribution indicates the mean value. B) Percentage composition of household sizes for each cluster.

M

Table 3: Trimodal Gaussian mixture model’s parameters.

an

Figure 3: Total annual consumptions distributions: A) Probability Density Function of metered HES243 dataset and trimodal Gaussian mixture fit. Each vertical bar at the bottom of the plot represents a data point. B) Empirical Cumulative Distributions of metered annual consumptions and trimodal Gaussian mixture fit. The dotted lines around the ECDF of the metered HES243 dataset are the 95% confidence bounds.

824

825

6.3. Individual appliances: Total annual consumptions

In order to gain a better insight into the relation-

826

We looked at the appliance content of the HES243

804

ship between household size and total annual con-

827

households and, based on the list of appliances of

805

sumption, we looked at the sub-groups of households

828

interest presented in Sec. 5.1, we grouped the house-

806

characterised by these features in two different ways.

829

holds that contained each one of those appliances.

807

Firstly, we grouped the households according to size,

830

We then calculated the ECDF of both simulated and

808

and used the KDE method to obtain an estimate

831

metered data for each one of those groups. Examples

809

of the empirical PDF corresponding to each group.

832

of the obtained distributions are shown in Fig. 5.

810

These distributions can be observed in Fig. 4(A).

833

The results of this analysis made evident that the

811

The number of households with 5 members is not

834

variability observed in the annual consumption of in-

812

large enough as to provide a reliable estimate of the

835

dividual appliances is completely misrepresented by

813

overall distribution of annual consumptions for this

836

the simulated data. In some cases (see Fig. 5(A)

814

sub-group. Therefore, this distribution was omitted.

837

and (D)) the average annual consumption of both

815

Secondly, based on the parametric estimate we ob-

838

datasets is well in agreement. In some others (Fig.

816

tained for the overall distribution, we grouped the

839

5(B) and (C)), the differences between the average

817

households according to the three observed clusters.

840

annual consumptions are evident as well.

818

The criteria for the allocation of households to the

819

different clusters was whether their annual consump-

Ac ce

pt

803

13

Page 13 of 21

ip t cr us an

Ac ce

pt

ed

M

Figure 5: Annual consumptions ECDFs of individual appliances: A) Main cooking appliances: cooker, or equivalently, hob+oven. Present in 70% of households. B) ECDFs of simulated and monitored kettles. Present in 94% of households. C) ECDFs of simulated and monitored washing machines. Present in 83% of households. D) ECDFs of simulated and monitored main TVs. Present in 98% of households.

14

Page 14 of 21

843

tions were skewed. Log-normal and Weibull models

844

were tested for possible fits, as these models are par-

845

ticularly good at representing skewed data.3 The

846

analysis revealed that the best fits were provided by

847

Weibull models. The summary of parameters of the

848

distributions fitted to the ECDFs of the annual con-

849

sumptions of individual appliances is presented in

850

Table 4. Table 4: Summary of parameters of the Weibull distributions fitted to the annual consumptions ECDFs of individual appliances.

Both the metered and simulated mean daily load

860

profiles have, generally speaking, similar shapes to

861

that of the typical profile. However, when the profiles

862

are compared in more detail, marked contrasts are

863

observed:

864

865

• There are significant differences between the values of the lowest and highest demands observed in the two profiles.

M

866

6.4. Mean daily load profile general features

pt

851

859

867

868

Mean daily load profiles were obtained from both

853

metered and simulated HES243 datasets. These can

854

be observed in Fig. 6, along with the typical UK pro-

855

file. This typical UK load profile corresponds to the

856

half hour load profile for the average Profile Class 1

857

customers4 [21], and is presented for comparison pur-

858

poses only.

Ac ce

852

3 A more empirical argument for the use of these models is rooted in the fact that they are generally applicable for modelling size/magnitude distributions (e.g. particle size, wind speed). 4 Profile Class 1 customers are domestic customers supplied on unrestricted tariffs, with a maximum demand below 100 kW as measured by metering systems containing only one meter register. There are eight profile classes, and for each profile class a sample group of electricity supply customers is randomly drawn from the population of electricity supply market customers. These samples are designed to provide an accurate estimate of the load pattern for each class of customers for use in electricity settlement. Consumption data is obtained by either installing half-hourly meters at the sites or getting half-hourly consumption data directly from suppliers.

• The simulated profile appears to overestimate the duration of the peak period.

869

• The variations observed in the CREST pro-

870

file, such as the transitions between periods of

871

low/high demand and periods of high/low de-

872

mand, correspond to more abrupt changes than

873

those observed in the other two profiles.

ed

Main cooking cooker oven microwave toaster kettle washing machine tumble dryer washer dryer dishwasher TV1 TV2 laptop desktop computer site

Weibull fit parameters Scale Shape 356.54 1.26 344.72 1.28 248.34 1.04 57.66 1.19 21.90 0.94 188.20 1.82 164.85 1.20 367.87 0.96 262.81 1.06 301.57 1.47 174.90 0.86 109.22 0.69 24.34 0.87 156.37 0.89 213.01 0.98

Figure 6: Mean daily load profiles corresponding to metered and simulated HES243 datasets. Typical UK profile corresponds to the load profile of the average class 1 (unrestricted domestic tariff) customer.

ip t

tributions of individual appliances’ annual consump-

cr

842

us

In general, it was observed that the empirical dis-

an

841

874

Further analysis of the characteristics and differ-

875

ences of these profiles may be desirable, and indeed,

876

necessary. In particular, it might be interesting to

877

pay a closer look at how the activity profiles and

878

the use of appliances are linked, and how well repre-

879

sented the duration of certain activities is. However,

880

a more detailed analysis of these profiles falls beyond

881

the scope of this paper. The prospects for a more de-

882

tailed study on the intra-day variability of demand

883

are left to be discussed in the next section.

884

7. Discussion and Future work

885

The primary aim of the analysis presented in

886

this paper was to determine whether a probabilistic

15

Page 15 of 21

model based on currently used approaches is capable

928

consumption across the whole 250 households HES

888

of providing a good representation of the variability

929

sample is just over 3% higher than the average across

889

observed in the electricity consumption levels of a

930

the HES243 dataset.

890

highly detailed dataset. The choice of the CREST

931

Great part of the analysis presented in this pa-

891

model for this study was due in great measure to

932

per focused on the distribution of households with

892

the fact that this model seeks to emulate the vari-

933

respect to their annual consumptions. The analy-

893

ability of household electricity use [18]. According

934

sis of the annual consumption data extracted from

894

to the way in which the model was constructed, the

935

the HES dataset revealed the existence of a complex

895

simulated appliances are configured such that their

936

trimodal distribution (see Sec. 6.2). Further analy-

896

annual consumptions result in figures typical of an

937

sis revealed that the underlying distribution appears

897

average household. Moreover, the overall average

938

to be very well estimated by a trimodal Gaussian

898

annual consumption of the simulated households was

939

mixture with analytical expression given by equa-

899

also expected to be in agreement with the national

940

tion (1).

900

figures. The model calibration involves the scaling of

941

the empirical distribution is consistent with a nor-

901

the simulated sample’s annual consumptions. This is

942

mal distribution. The resultant composite distribu-

902

meant to ensure that the simulated average annual

943

tion, however, does not exhibit normal-like features.

903

consumption matches the average annual consump-

944

904

tion of the real-life counterpart (see Sec. 3).

945

cr

ip t

887

an

us

Each of the three clusters identified in

A breakdown into sub-groups of households characterised by size revealed that: 1) Over 50% of the households concentrated around the first cluster are

The high level of detail offered by HES data justi-

946

906

fies its use for the analysis. The appliance-level me-

947

one-person households. The first cluster is also the

907

tered electricity consumption records make it ideal

948

largest one, which means that the majority of the

908

for a comparison against the simulated appliance

949

one-person households are found in this consump-

909

consumption data. Due to the technical limitations

950

tion range.

910

of the model discussed in Section 6, the original HES

951

centrated around the second cluster correspond to

911

dataset had to be filtered so as to allow for a con-

952

two-people households, making this sub-group the

912

sistent analysis. The filtering consisted in removing

953

predominant one. 3) Over 33% of the households

913

the households with more than five members from

954

concentrated around the third cluster are 4-people

914

the sample. However, we believe this filtering had

955

households. The second biggest group corresponds

915

little impact on the overall statistical characteristics

956

to two-people households (see Fig. 4). It appears to

916

of the dataset and the analysis results. The propor-

957

be a linear correlation between the household size of

917

tions of households in the HES sample correspond-

958

the predominant group and the mean value of the

918

ing to household sizes ranging from 1 to 4 are well

959

corresponding cluster. However, further analysis is

919

in agreement with the proportions observed at the

960

needed in order to determine whether this is a gen-

920

national level [14]. If we extrapolate this, by assum-

961

eral trend or just an interesting coincidence.

921

ing that the proportion of households with five and

962

The distributions of the simulated annual con-

922

6+ residents are equally well represented in the sam-

963

sumptions were found to be consistently normal. It

923

ple, this would mean that households with 6 or more

964

would appear that the current simplifying modelling

924

members account for just over 2% of households in

965

assumptions are causing simulation outputs consis-

925

the UK. A sense of the scale of the effect of removing

966

tent with normally distributed data. These assump-

926

said households can be given by comparing the over-

967

tions would appear to lead to reasonable first-order

927

all average annual consumptions; the average annual

968

estimates as misrepresentation issues appear less se-

Ac ce

pt

ed

M

905

16

2) Over 40% of the households con-

Page 16 of 21

969

vere when simulations are restricted to small sets of

1010

transform sampling. Given a cumulative distribu-

970

households. However, the differences between simu-

1011

tion function, this method allows for the generation

971

lated and metered data become evident when simu-

1012

of samples consistent with data drawn from said dis-

972

lating larger samples.

1013

tribution. A better idea of the statistical characteris-

Modelling assumptions concerning the conversion

1014

tics of the distribution of annual consumptions gives

974

of activity profiles into electricity consumption pat-

1015

us the opportunity to fine tune demand models. The

975

terns have remained essentially the same over the

1016

improvements derived from this would be reflected in

976

last decade. It is therefore necessary to reassess these

1017

simulated datasets that are more in agreement with

977

assumptions. Assumptions leading to normally dis-

1018

the kind of distribution and levels of variability ob-

978

tributed data will need to be modified or replaced

1019

served across real-life households.

979

entirely. If replacing these assumptions in their en-

1020

Total annual consumptions from individual appli-

980

tirety proves overly complicated, then the implemen-

1021

ances were used as a further point of comparison

981

tation of mixture models based on normal compo-

1022

between simulated and metered datasets. Based on

982

nents might be a good alternative.

1023

each dataset, distributions of total annual consump-

us

cr

ip t

973

In addition to the differences in the overall shape

1024

tions were obtained for the appliances listed in Ta-

984

of the distributions, it was observed that the variabil-

1025

ble 1. The choice of the appliances of interest was

985

ity in the levels of annual consumption is consistently

1026

986

misrepresented in the simulated data. Regardless of

1027

987

sample size, it was found that the level of variabil-

1028

988

ity observed in the metered data is consistent across

1029

tor is calculated for each appliance. According to the

989

independent datasets. Moreover, the variability ob-

1030

model documentation, this factor is adjusted so that

990

served in the metered data is about 20% higher than

1031

over a large number of runs the average annual con-

991

in the simulated data (see Table 2). The HES sample

1032

sumption of the appliance would match typical levels

992

is still arguably small, statistically speaking. How-

1033

[18]. In some cases it was found that the average an-

993

ever, we presume it provides a better insight into the

1034

nual consumption of the simulated appliances was

994

kind of distribution and variability that would be

1035

well in agreement with that of their metered coun-

995

observed in larger samples. Given the method used

1036

terparts (see Fig. 5(A) and (D)). In most cases, how-

996

for estimating the overall distribution, it is also very

1037

ever, discrepancies were found. In general, the sim-

997

likely that the statistical characteristics observed in

1038

ulated values are consistently higher than those ob-

998

the estimate are close to those of the true population

1039

tained from the metered data. In terms of the distri-

999

distribution. It is important that a refined represen-

1040

bution, similar problems to those of observed in the

1000

tation of the characteristics of the distributions ob-

1041

distributions of total household annual consumptions

1001

served in Fig. 3 is achieved, as this is key to a robust

1042

were found. The variability observed in the metered

1002

approach to residential electricity demand modelling.

1043

data is consistently under-represented by the simula-

1003

The analysis of the distribution of metered annual

1044

tions’ output. Moreover, the annual consumptions of

1004

consumptions generated many interesting results,

1045

individual simulated appliances present skewed dis-

1005

which include analytic expressions for the probability

1046

tributions. These distributions were found to be con-

1006

density function (PDF) and the cumulative distribu-

1047

sistent with Weibull distributions. A summary of the

1007

tion function (CDF) (see Sec. 6.2). Knowing the

1048

parameters for the fitted models is presented in Table

1008

analytical expression for the cumulative distribution

1049

4.

1009

allows for the use of methods such as the inverse

1050

an

983

based on the reasonable expectation that their demand loads would be linked to households activities.

Ac ce

pt

ed

M

In the CREST model’s simulations, a calibration fac-

17

A comparison was also made between metered and

Page 17 of 21

simulated mean daily load profiles extracted from

1090

ancies were found when the corresponding distribu-

1052

the corresponding HES243 datasets. Important dif-

1091

tions were compared (see Figs. 2 & 5). In particu-

1053

ferences in the overall features of both profiles were

1092

lar, it was found that metered household annual con-

1054

identified. Further in-depth analysis is needed in or-

1093

sumptions follow a complex distribution from which

1055

der identify the underlying causes of these issues.

1094

three clusters can be identified. The distributions ob-

1056

However, a more detailed characterisation of said

1095

served in the simulated data are much simpler. Cur-

1057

differences falls beyond the scope of this paper. In

1096

rent underlying assumptions about electricity use ap-

1058

particular, it would be interesting to investigate in

1097

pear to lead to normally distributed data with consis-

1059

more detail the relationship between household ac-

1098

tently limited variability. Therefore, these assump-

1060

tivity patterns, appliance usage and the intra-day

1099

tions need to be rectified so as to prevent the misrep-

1061

variations in demand levels. This will be the subject

1100

resentation of the statistical characteristics observed

1062

of future work.

1101

in metered data.

1063

8. Conclusions

us

cr

ip t

1051

1102

The diversity of real-life households is reflected by the complexity of the distribution of total an-

In this paper, a comparative analysis of the sta-

1103

1065

tistical characteristics of metered and stochastically

1104

1066

simulated electricity consumption datasets was pre-

1105

1067

sented. Metered household- and appliance-level elec-

1106

1068

tricity consumptions were extracted from the UK’s

1107

a trimodal Gaussian mixture model which provides

1069

Household Electricity Survey dataset (see Sec. 4).

1108

a very good estimate of the observed distribution.

1070

Corresponding electricity consumptions were simu-

1109

Analytical expressions for both the density function

1071

lated using a widely implemented probabilistic model

1110

and cumulative distribution are given. In a similar

1072

based on the UK residential sector (see Sec. 3). The

1111

manner, the distributions of annual consumptions of

1073

model was configured such that the simulated house-

1112

individual appliances were found to be well repre-

1074

holds matched the relevant features of the metered

1113

sented by Weibull models. As this paper demon-

1075

counterparts. The analysis of the differences between

1114

strates, it is possible to use estimates that capture

1076

datasets allowed us to provide a measure of how well

1115

reasonably well the complexity of the observed dis-

1077

represented are the observed features by probabilis-

1116

tribution while preserving models’ simplicity.

1078

tic models based on currently used approaches and

1079

to identify key shortcomings.

an

1064

nual consumptions. A more complex distribution does not necessarily mean over-complicated assump-

Ac ce

pt

ed

M

tions need to be used in the models. We propose

1080

In particular, we compared the way simulated and

1117

The analysis presented shows that residential de-

1081

metered households and individual appliances are

1118

mand for electricity is more diverse than hitherto

1082

distributed with respect to total annual consump-

1119

assumed. A better idea of how households and in-

1083

tions. An element of the assessment of the model’s

1120

dividual appliances are distributed with respect to

1084

performance concerns how well represented are these

1121

annual consumption provides us with opportunities

1085

distributions by the simulated output.

Based on

1122

for further refinement of current probabilistic mod-

1086

the analysis presented in this paper we can con-

1123

els. In addition, the results further support the fact

1087

clude that current probabilistic models fail to cap-

1124

that current and future modelling approaches would

1088

ture some of the key characteristics observed in the

1125

benefit greatly from the use of larger, highly resolved

1089

metered datasets (see Sec. 6.2). Significant discrep-

1126

metered datasets.

18

Page 18 of 21

[6] EA Technology, 2012. Assessing the impact

Acknowledgements

of low carbon technologies on Great Britain’s

This work was partially supported by the Consejo

power distribution networks. Tech. rep., Ofgem.

Nacional de Ciencia y Tecnolog´ıa (CONACyT).

URL

https://www.ofgem.gov.uk/

publications-and-updates/assessing-

References

impact-low-carbon-technologies-great[1] Aerts, D., Minnen, J., Glorieux, I., Wouters,

britains-power-distribution-networks

I., Descamps, F., 2014. A method for the [7] Energy Saving Trust, DECC, DEFRA, Owen,

ip t

identification and modelling of realistic domes-

P., 2012. Powering the nation:

Household

demand simulations and peer comparison.

electricity-using habits revealed. Tech. rep.,

Build. Environ. 75, 67–78.

Energy Saving Trust, Department of Energy

URL

and Climate Change, Department for Environ-

cr

tic occupancy sequences for building energy

http://dx.doi.org/10.1016/j.

ment Food and Rural Affairs, London, United

us

buildenv.2014.01.021

Kingdom. [2] Ballanti, A., Ochoa, L. F., 2015. Initial assess-

URL

ment of voltage-led demand response from UK

an

uk/Publications2/Corporate/Research-

residential loads. In: 2015 IEEE Power Energy

and-insights/Powering-the-nation-

Soc. Innov. Smart Grid Technol. Conf. IEEE,

URL

household-electricity-using-habits-

M

pp. 1–5.

http://www.energysavingtrust.org.

revealed

http://dx.doi.org/10.1109/ISGT.

[8] Good, N., Zhang, L., Navarro-Espinosa, A.,

ed

2015.7131821

[3] Ballanti, A., Pilo, F., Navarro-Espinosa, A.,

Ochoa, L. F., 2013. Assessing the benefits of

pt

PV var absorption on the hosting capacity of

Mancarella, P., 2015. High resolution modelling of multi-energy domestic demand profiles. Appl. Energy 137, 193–210. URL

http://dx.doi.org/10.1016/j.

LV feeders. In: IEEE PES ISGT Eur. 2013.

URL

apenergy.2014.10.028

Ac ce

IEEE, pp. 1–5.

[9] Ipsos-RSL, September 2003. Ipsos-RSL and Of-

http://dx.doi.org/10.1109/

fice for National Statistics, United Kingdom

ISGTEurope.2013.6695423

Time Use Survey, 2000 [computer file]. 3rd Edi-

[4] Bondu, A., Dachraoui, A., 2015. Realistic and

tion. Colchester, Essex: UK Data Archive [dis-

very fast simulation of individual electricity

tributor], SN: 4504, URL http://dx.doi.org/

consumptions. In: 2015 Int. Jt. Conf. Neural

10.5255/UKDA-SN-4504-1.

Networks. IEEE, pp. 1–8. URL

[10] McKenna, E., Thomson, M., 2016. High-

http://dx.doi.org/10.1109/IJCNN.

resolution stochastic integrated thermalelectri-

2015.7280339 [5] DECC, 2015. Chapter 3:

cal domestic demand model. Appl. Energy 165,

Domestic energy

445–461.

consumption. In: Energy Consum. UK. Depart-

URL

ment of Energy and Climate Change, London,

http://dx.doi.org/10.1016/j.

apenergy.2015.12.089

United Kingdom, Ch. 3, p. 17. https://www.gov.uk/government/

[11] Navarro, A., Ochoa, L., Mancarella, P., Ran-

statistics/energy-consumption-in-the-uk

dles, D., 2013. Impacts of photovoltaics on low

URL

19

Page 19 of 21

voltage networks: a case study for the north

Cambridge, United Kingdom.

west of England. In: 22nd Int. Conf. Exhib.

URL

Electr. Distrib. (CIRED 2013). Institution of

publications/household-electricity-

Engineering and Technology, pp. 1419–1419.

survey--2

URL http://dx.doi.org/10.1049/cp.2013.

https://www.gov.uk/government/

[17] Richardson, I., Thomson, M., Infield, D., 2008.

1229

A high-resolution domestic building occupancy model for energy demand simulations. Energy

[12] Office for National Statistics, 2003. The United

Build. 40 (8), 1560–1566.

port. Tech. rep., Office for National Statistics,

URL

London, United Kingdom.

enbuild.2008.02.006

http://www.ons.gov.uk/ons/rel/

https://dx.doi.org/10.1016/j.

cr

URL

ip t

Kingdom 2000 Time Use Survey: Technical Re-

[18] Richardson, I., Thomson, M., Infield, D., Clifford, C., 2010. Domestic electricity use: A

use-survey--technical-report.pdf

high-resolution energy demand model. Energy

us

lifestyles/time-use/2000-edition/time-

Build. 42 (10), 1878–1887.

[13] Ofgem, 2015. Typical Domestic Consumption

URL

URL

https://dx.doi.org/10.1016/j.

an

Values for gas and electricity 2015.

enbuild.2010.05.023

https://www.ofgem.gov.uk/gas/

retail-market/monitoring-data-

[19] Swan, L. G., Ugursal, V. I., 2009. Modeling of

and-statistics/typical-domestic-

M

end-use energy consumption in the residential

consumption-values

sector: A review of modeling techniques. Renew. Sustain. Energy Rev. 13 (8), 1819–1835.

[14] ONS, 2015. Families and Households: 2015.

URL https://dx.doi.org/10.1016/j.rser.

don, United Kingdom.

2008.09.033

URL

ed

Tech. rep., Office for National Statistics, Lon-

pt

http://www.ons.gov.uk/

[20] Torriti, J., 2014. A review of time use models of residential electricity demand. Renew. Sustain.

birthsdeathsandmarriages/families/

Energy Rev. 37, 265–272.

Ac ce

peoplepopulationandcommunity/

bulletins/familiesandhouseholds/2015-

URL

11-05

2014.05.034

http://dx.doi.org/10.1016/j.rser.

[15] Page, J., Robinson, D., Morel, N., Scartezzini,

[21] UKERC Energy Data Centre, Electricity Asso-

J.-L., 2008. A generalised stochastic model for

ciation, Elexon Ltd., 2013. Electricity user load

the simulation of occupant presence. Energy

profiles by profile class. Tech. rep., Electricity

Build. 40 (2), 83–98.

Association, London, United Kingdom.

URL

URL http://data.ukedc.rl.ac.uk/browse/

http://dx.doi.org/10.1016/j.

enbuild.2007.01.018

edc/Electricity/LoadProfile/doc

[16] Palmer, J., Terry, N., Kane, T., Firth, S.,

[22] Wahba, G., 1975. Optimal Convergence Prop-

Hughes, M., Pope, P., Young, J., Knight, D.,

erties of Variable Knot, Kernel, and Orthogonal

Godoy-Shimizu, D., 2013. Electrical appliances

Series Methods for Density Estimation. Ann.

at home: tuning in to energy savings. Tech.

Stat. 3 (1), 15–29.

rep., Cambridge Architectural Research —

URL

Element Energy — Loughborough University,

1176342997 20

https://dx.doi.org/10.1214/aos/

Page 20 of 21

[23] Wid´en, J., Molin, A., Elleg˚ ard, K., 2012. Models of domestic occupancy, activities and energy use based on time-use data:

deterministic

and stochastic approaches with application to various building-related simulations. J. Build. Perform. Simul. 5 (1), 27–44. URL

http://dx.doi.org/10.1080/

ip t

19401493.2010.532569 [24] Wid´en, J., W¨ ackelg˚ ard, E., 2010. A highresolution stochastic model of domestic activity

cr

patterns and electricity demand. Appl. Energy 87 (6), 1880–1892. URL

us

https://dx.doi.org/10.1016/j.

apenergy.2009.11.006

an

[25] Wilke, U., Haldi, F., Scartezzini, J.-L., Robinson, D., 2013. A bottom-up stochastic model

activities. Build. Environ. 60, 254–264. URL

M

to predict building occupants’ time-dependent

http://dx.doi.org/10.1016/j.

ed

buildenv.2012.10.021

[26] Yao, R., Steemers, K., 2005. A method of formulating energy load profile for domestic

663–671.

https://dx.doi.org/10.1016/j.

Ac ce

URL

pt

buildings in the UK. Energy Build. 37 (6),

enbuild.2004.09.007

[27] Zimmermann, J.-P., Evans, M., Griggs, J., King, N., Harding, L., Roberts, P., Evans, C., 2012. Household Electricity Survey: A study of domestic electrical produc usage - Final report. Tech. rep., Intertek, London, United Kingdom. URL http://randd.defra.gov.uk/Default. aspx?Menu=Menu&Module=More&Location= None&ProjectID=17359&FromSearch= Y&Publisher=1&SearchText=EV0702& SortString=ProjectCode&SortOrder=Asc& Paging=10#Description

21

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