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This is a pre-print of the published article Roberts, M.B., N. Haghdadi, A. Bruce and I. MacGill, Characterisation of Australian apartment
electricity demand and its implications for low-carbon cities. Energy, 2019. 180: p. 242-257.
DOI: 10.1016/j.energy.2019.04.222
Cluster-based characterisation of Australian apartment
electricity demand and its implications for low-carbon cities
Mike B Roberts a,b,
1
, Navid Haghdadi a,c, Anna Bruce a,b and Iain MacGill a,c
a Centre for Energy and Environmental Markets,
b School of Photovoltaics & Renewable Energy Engineering,
c School of Electrical Engineering and Telecommunications,
University of New South Wales, Sydney, NSW 2052, Australia
Abstract
Understanding of residential electricity demand has application in efficient building design, network planning
and broader policy and regulation, as well as in planning the deployment of energy efficiency technologies and
distributed energy resources with potential emissions reduction benefits as well societal and household cost
savings. Very few studies have explored the specific demand characteristics of apartments, which house a
growing proportion of the global urban population.
We present a study of apartment electricity loads, using a dataset containing a year of half-hourly electricity
data for 6000 Australian households, to examine the relationship between dwelling type, demographic
characteristics and load profile. The focus on apartments, combined with the size of the data set, and the
representative seasonal load profiles obtained through clustering full annual profiles, is unique in the literature.
We find that median per-occupant household electricity use is 21% lower for apartments than for houses and
that, on average, apartments have lower load factor and higher daily load variability, and show greater diversity
in their daily peak times, resulting in a lower coincidence factor for aggregations of apartment loads. Using
cluster analysis and classification, we also show the impact of dwelling type on the shape of household electricity
load profiles.
Keywords
Apartments; Residential electricity demand; Load profiles; Cluster analysis; Load aggregation; low-carbon cities
1. Introduction
The Paris Agreement that emerged from COP 21 in December 2015 commits the world to “pursuing efforts” to
limit average global temperature to 1.5ºC above pre-industrial levels by reducing anthropogenic greenhouse gas
(GHG) emissions [1]. Globally, residential buildings are responsible for 13% of end energy use and 28% of
electricity use [2], while the IEA estimates that keeping average temperature rises to 1.5ºC requires “virtually
all” residential and commercial buildings to achieve net-zero emissions by 2040 [3].
In the absence of coherent national policies, numerous Australian cities have adopted ambitious carbon
reduction targets [4-6], but achieving these reductions in the residential sector is complex, involving
consideration of embodied and operational energy in residential buildings, as well as wider energy use to deliver
services such as transport. The residential sector as a whole is currently responsible for an estimated 11% of
Australia’s total final energy use [7]. As in many countries, increasing population is driving compact city planning
strategies across Australia, with the number of occupied residential dwellings forecast to rise to almost ten
million by 2020, an increase of 61% since 1990 [8]. While 14% of all Australian dwellings are currently
Abbreviations: ABS, Australian Bureau of Statistics; ADMD, After Diversity Maximum Demand; BOM, Bureau of Meteorology;
CER, Commission for Energy Regulation; CF, Coincidence Factor; CV, Coefficient of Variation; HVAC, Heating, ventilation, and
air conditioning; LF, Load Factor; MLR, Multinomial Logistic Regression; NMI, National Meter Identifier; NSW, New South
Wales; PCA, Principal Component Analysis; PCA, Profile Class; PV, Photovoltaic; RFE, Recursive Feature Elimination; SCM,
Self-Consumption Metric; SGSC, Smart Grid Smart City.
1
Corresponding author: m.roberts@unsw.edu.au
This is a pre-print of the published article Roberts, M.B., N. Haghdadi, A. Bruce and I. MacGill, Characterisation of Australian apartment
electricity demand and its implications for low-carbon cities. Energy, 2019. 180: p. 242-257.
DOI: 10.1016/j.energy.2019.04.222
apartments
2
[9] and these house 10% of the population, apartments now comprise one third of all new
residential buildings [10]. Although much has been written [11-14] about the implications for energy use and
carbon emissions of increasing housing density including this move to greater apartment living, there is still a
lack of clear consensus, due in part to a lack of detailed analysis of operational energy loads across the diverse
range of multi-occupancy residential buildings, and their comparison with stand-alone housing.
3
A greater understanding of operational energy use in this sector, particularly of the temporal variability of
electricity loads, diversity across different building types and between households, and the differential effects
of demand aggregation between stand-alone homes and apartments, can better inform regulation and design
strategies for residential buildings and urban developments. One clear opportunity is to assist network operators
in forecasting capacity requirements for augmentations, replacements and new developments. More generally,
it could also help to identify suitable opportunities for distributed energy resources such as photovoltaic (PV)
generation, storage, energy efficiency and flexible residential loads to contribute to shaping individual or
aggregated household demand in order to reduce household and network energy expenditure, while reducing
urban climate change emissions and supporting the transition to low carbon cities.
Increased availability of individual household load data with high temporal resolution, as residential
accumulation meters are replaced by smart or interval meters, offers an opportunity to extend this
understanding. In Australia, however, policies for deployment of these meters are inconsistent between states
and between electricity utilities [16, 17]. Even where suitable meters are widespread and high quality data is
available to Network Service Providers and retailers, concerns about customer consent, confidentiality and data
protection [18] can result in data that is hard to access or dislocated from information about household
characteristics or dwelling type.
Smart Grid Smart City (SGSC) [19] was a major Australian project aimed at assessing the impact of a range of
demand response products, including tariff structures and energy monitoring tools, on residential customers’
energy use. Household level 30-minute interval load data was collected and made publicly available for some
13,700 residential customers across New South Wales over a three-year period and a subset of this dataset
containing a complete year of data (allowing analysis of seasonal variations) for approximately 6000 households
has been utilised for this study. Crucially, this subset includes some 2000 apartment households, enabling a
detailed comparison between dwelling types, an assessment of the diversity of load profiles between different
apartments and an analysis of the effects of aggregating loads for each type of dwelling. This combination of a
large household dataset, associated demographic survey information, and the use of clustering to derive
representative load profiles from 12 months of interval meter data has not been applied to multi-occupancy
dwellings in the literature to date.
The rest of this paper is structured as follows. Section 2 provides a brief review of previous studies analysing
household load profiles, both internationally and in Australia. In light of the global growth in apartment living, it
is interesting to note that the literature contains little specific analysis of apartment electricity demand, either
in comparison to stand-alone housing or with respect to the diversity of building and household characteristics
found in this housing sector. Our emphasis on the distinct characteristics of apartment demand is therefore
somewhat novel and may be useful in drawing out detail pertinent to electricity networks that are adapting to
evolving urban landscapes as well as transitioning towards distributed and low-carbon generation. Section 3
introduces the dataset used for this study and summarises the processes used to select households and to
prepare the data. In section 4, we compare average (total and per capita) energy demand for apartments and
houses and examine features of their average daily load profiles. In section 5, we assess the temporal variability
of the annual load profiles, using a range of metrics pertinent to assessing network impacts and to designing PV
and battery storage systems, and examine the effect of aggregation on these metrics for apartments and for
houses. In section 6, we present the results of a cluster analysis, carried out to categorise the annual household
2
The terms ‘Apartment’ and ‘Unit’ are used interchangeably in this paper
3
It is important to note that apartment building electricity use combines common property loads and individual apartment
loads. Common property loads are highly variable across Australia’s diverse building stock 15. Roberts, M.B., et al.,
Using PV to help meet common property energy demand in residential apartment buildings, in Australian Summer Study in
Energy Productivity. 2016: Sydney. and, although negligible for many two- or three-storey ‘walk-ups’, can be responsible for
a large proportion of total building energy use in high-rise tower blocks, where they may include lifts, carpark ventilation and
lighting, water heating and pumping for pools and centralised HVAC and water heating for apartments, as well as lighting for
stairwells, corridors and other common areas.
This is a pre-print of the published article Roberts, M.B., N. Haghdadi, A. Bruce and I. MacGill, Characterisation of Australian apartment
electricity demand and its implications for low-carbon cities. Energy, 2019. 180: p. 242-257.
DOI: 10.1016/j.energy.2019.04.222
load profiles and relate them to a range of household characteristics. Finally, in Section 7, we discuss our results,
draw some tentative conclusions regarding the energy and hence emissions performance of apartments,
aggregate demand network impacts as well as their potential suitability for PV and other distributed energy
options compared to stand-alone housing, and suggest possible areas for further study.
2. Previous work
Approaches to the analysis of residential electricity consumption are generally categorised according to the type
and level of data used. Top-down approaches use high level aggregated data at the scale of substations or the
wider network, while bottom-up approaches use metered electricity load data at a household level or synthesise
household loads from appliance usage statistics and physical models of dwelling performance.
A comprehensive review of models for predicting household energy loads is outside the scope of this paper, and
a number of such reviews can be found in the literature [20-26] . Instead, the following summary is focussed on
studies that apply cluster analysis to high resolution load profiles and those that are specific either to apartment
loads or to the Australian context.
2.1 Energy use and household characteristics
Annual household load profiles are dependent on multiple factors including dwelling characteristics, climate,
household demographics, appliance ownership and cultural modes of energy use [27]. A considerable number
of studies have examined this relationship but, whether by necessity (reliance on low temporal resolution data,
such as electricity bills) or by design, many of these studies [28-35] characterise household energy use by the
total (or average daily) energy demand, without consideration of the temporal variation of the load. More
recently, widespread deployment of interval meters for residential customers has resulted in increasing
availability of high-resolution household load data [20] with sampling periods ranging from one minute to an
hour, which can be used to identify the contribution of individual appliances to overall load [36-38] for
forecasting, including to predict the contribution of individual appliances to peak electricity demand, measured
either at the time of the customer’s peak, or relative to aggregate or network peaks [39], and for load
management, both customer classification and implementation of demand response [40].
In Australia, energy bills and Australian Bureau of Statistics (ABS) household expenditure data have been used
to model household energy use in Sydney [41], and to estimate New South Wales aggregated electricity
consumption at the census collection district level [42]. Due to the sporadic deployment of residential smart
meters across Australia, as well as privacy concerns (see Section 0), more detailed analysis of residential
electricity load profiles in Australia has been limited by the small number of published datasets containing
residential customer load data at high temporal resolution.
The Smart Grid Smart Cities dataset used for this paper (see Section 3) has been the subject of a number of other
studies [20, 29, 39, 43, 44]. Fan et al. [29, 39] used the data to create a linear regression model relating household
characteristics to average daily demand and to peak demand. One of their conclusions was that detached and
semi-detached houses have higher average daily electricity demand than apartments [29] and that, during the
12 maximum peak demand periods in the financial year 2013, average detached house loads were
approximately twice those of apartments
4
[39]. Elsewhere, the dataset has been used to propose a strategy for
demand response to address peak load caused by air conditioning [38]. Looking at temporal variability of the
load profiles, Motlagh et al. [44] applied clustering and principal component analysis (PCA) techniques to 30-day
profiles for 1800 of the SGSC customers to assess the impact of the dynamic peak pricing and dynamic peak
rebate tariffs on the load profiles.
2.2 Cluster analysis
Cluster analysis is a commonly-used data mining technique that can be used to group energy load profiles in
order to identify characteristics common to groups of households. Overviews of different clustering techniques,
as commonly applied to aggregated residential loads or to individual commercial loads, are available in the
literature [20, 45]. However, the application of clustering to individual residential loads is less common due to
reliance on a small group of published datasets. In a US study [46], daily profiles of 85 customers were clustered
and then each customer was characterised by the proportion of their daily profiles to be found in each cluster.
Irish researchers [47] have used a similar approach, applying clustering techniques to each daily profile of 3941
4
Detached house loads were between 98% and 107% more than apartment loads, depending on the use and type of air-
conditioning in the household
This is a pre-print of the published article Roberts, M.B., N. Haghdadi, A. Bruce and I. MacGill, Characterisation of Australian apartment
electricity demand and its implications for low-carbon cities. Energy, 2019. 180: p. 242-257.
DOI: 10.1016/j.energy.2019.04.222
households, drawn from a dataset collected by the Commission for Energy Regulation (CER), over a six-month
period, assigning each customer to one of ten profile classes (PC) based on the modal PC of its daily profiles, and
then describing the relationship between profile class and household characteristics.
Rhodes et al. [48], using one-minute load data from 103 Texan households, clustered the seasonal profiles
(rather than daily profiles) of customers (a technique elsewhere applied to the CER dataset [49]) and applied a
regression analysis to relate the clusters to household characteristics. However, as the paper does not reference
dwelling type, it is not clear whether any of the households were apartments.
In their CSIRO report for Queensland electricity network operator Energex, Berry et al. [50] examined 5 datasets.
Load profiles for 1871 customers across three of the datasets were grouped into clusters according to daily load
shape and seasonal trends, identifying five core clusters and three smaller outliers. Separately, 921 households
from a single dataset were segmented according to demographic characteristics (dwelling type, household
composition and income), their load profiles clustered within each segment, and a single profile chosen as being
representative of each cluster. With up to three clusters within each of eight segments, group sizes were small,
although some of these intra-segment clusters showed strong alignment with the clusters derived from the
larger dataset. However, as the sample contained only 34 households not living in detached houses, the report
is not able to draw strong conclusions about the relationship between profile and dwelling type, except to say
that the largest cluster of non-detached dwellings has the lowest typical demand of all the segments. Also in
Australia, Yildiz et al. [51] developed a clustering approach to classify households with rooftop PV according to
their daily load and PV generation profiles, in order to assist in forecasting self-consumption, import and export.
2.3 Apartment energy use
Most of the studies mentioned above are either based on houses or do not specifically consider dwelling type.
A small number of studies have directly addressed the relationship between household loads and dwelling type,
but the conclusions drawn are limited and sometimes contradictory.
An international review of factors affecting domestic energy consumption [52] cites the conclusion of a number
of studies in the UK, the Netherlands, Ireland, Portugal and the USA, that apartments use less energy than
detached dwellings. Amongst studies that include dwelling type as a potential factor in energy use, many have
found that total electricity consumption increases with the degree of detachment [26, 53-57], although one [58]
did not include apartments in the analysis. Others have been less conclusive, finding no relationship between
dwelling type (other than mid-terrace houses) and high electricity consumption in UK dwellings [52], or lower
consumption of gas or other fuels in apartments, but no significant difference in electricity consumption [59,
60]. Others [61] argue that, because dwelling size is correlated to size of household, the effect of dwelling type
on energy use is covered by these factors (houses use more energy because they are larger than apartments),
and so does not require explicit consideration. However, a study of dwellings in urban and rural Finland [62]
found that, although average energy use in apartments is significantly lower than in houses, apartment per
capita energy use is only slightly lower in rural areas, and in urban areas is higher in apartments than per capita
energy use in houses.
Although the Irish CER dataset used in a number of studies [27, 47, 63, 64] included only 67 apartments amongst
over 4000 residential dwellings, one of the studies [27], examining the dependence of four load parameters on
household characteristics for 4200 households, found apartments to have a significant negative impact on total
load and maximum demand. However, no significant correlation was found between load factor or time of peak
demand and apartment dwellings, (although terraced and semi-detached houses showed a significant negative
impact on load factor, compared to detached dwellings).
Two commonly cited Australian studies give conflicting views of the relationship between dwelling type and
energy use. A 2010 IPART study [32] suggests that apartments use less total energy (gas and electricity) than
detached dwellings. Although this study does not consider apartment building common property loads, these
are likely to be significant only for the 8% of the apartments surveyed that were in buildings of three storeys or
more [65]. A 2005 study by Energy Australia [35] is very often quoted as finding that high rise apartments and
detached houses have higher energy use than low or medium rise apartments and that per-capita energy
emissions are highest in high-rise apartment buildings and higher in mid- and low-rise apartment buildings than
in detached houses, although it is unclear whether these emissions calculations are based solely on total energy
use or consider the energy sources utilised.
This is a pre-print of the published article Roberts, M.B., N. Haghdadi, A. Bruce and I. MacGill, Characterisation of Australian apartment
electricity demand and its implications for low-carbon cities. Energy, 2019. 180: p. 242-257.
DOI: 10.1016/j.energy.2019.04.222
In contrast, a detailed analysis of datasets from several studies, including the IPART report, [65] estimated that
energy use in low-rise attached dwellings is 15-20% lower than in detached dwellings, but allowed the possibility
that dwelling type may, to some degree, act as a proxy for dwelling size. The same analysis also suggests that
the apparent high energy use of high-rise apartments attributed to the Energy Australia report may be due to
the presence of “luxury common area features”. Previous work by the authors [15] highlighted the diversity of
common property demand which can present a significant opportunity for renewable generation and demand
management.
Given the lack of concrete conclusions on apartment loads, it is unsurprising that there is high variability in the
consideration given to dwelling type by Australian Network Service Providers when estimating ‘After Diversity
Maximum Demand’ (ADMD), the average customer contribution to aggregated peak demand. For example, in
Western Australia, Western Power use ADMD values of 3.1 – 5.4kVA for apartments in buildings with more than
ten dwellings, compared to 4.7 – 8.7 kVA for detached dwellings [66], while in NSW, Endeavour Energy use
values of 6.5 or 7.5kVA for apartments (in areas with and without gas supplies, respectively), the same as the
value for small (and in most areas for medium) detached houses [67].
3. Data source and preparation
3.1 Dataset
This study utilises a dataset [68] of 30-minute interval load data from households across eight local government
areas in New South Wales (NSW), collected for the Smart Grid Smart City (SGSC) Project. Details of the project
and dataset are provided by Motlagh et al. [44], and in the SGSC Executive Report [19] and SGSC Technical
Compendia [69-71], with additional information about the customer selection process contained in the ‘Futura
Report’ [72]. Of the 78,000 households involved in the study, 13,735 provided some interval load data between
2011 and 2014, with the highest concentration of data collected during the calendar year 2013. This period was
therefore chosen for the analysis, with customers excluded from the dataset if more than 10% of their data was
missing or zero
5
over the period.
For the SGSC study, the type of dwelling for each customer was inferred from the number of ‘National Meter
Identifiers’ (NMI)
6
at the core address – if there were six or more NMIs, the dwelling was designated as ’Unit’; if
less than six, as ‘Not Unit’ (i.e. detached or semi-detached houses). As these inferences were correct in 96% of
cases where a sales agent visited the dwelling [71], the ‘assumed dwelling type’ has been used for much of this
analysis.
3.2 Data selection
The SGSC project involved trialling a number of tariff structures (seasonal time of use, dynamic peak pricing and
dynamic peak rebate) and customer feedback products (online portal, home energy monitor and appliance
control) to investigate their impact on customer load and peak demand. Some of the load data was therefore
influenced by participation in the trials. In order to reduce this influence, three groups of households have been
selected from the SGSC trials: the ‘control’ group of 1809 customers who were supplied with a smart meter but
not offered any of the trial products; 3164 customers supplied with a smart meter who declined all products
offered to them; and 1150 customers who were supplied with smart meters and access to an online portal to
monitor energy use, but no other products. (For this latter group, the SGSC study found that the impact of the
trial on energy use and peak demand were only 0.1% and -0.7% respectively [69]. Of these customers, a further
89 (including 23 from the control group) who were identified as having net metering for solar generation were
removed from the dataset. The geographic area of the dataset includes two climate zones, with 79% of
households in the Warm Temperate regions near the NSW coast and 21% in the Mild Temperate regions further
inland.
Although precautions were taken to ensure the initial SGSC customer group was representative of the wider
population [71], the various methods used to sell customers each of the demand response products are likely
to have resulted in selective biases within each of the product groups. The control group (of 1786 customers) is
therefore the only group that can be considered to be more broadly representative of the customer population,
5
Zero values in the dataset represent loads less than 2W and are most likely to be empty dwellings or missing data as most
households have at least one appliance on standby which would exceed this value 73. Equipment Energy Efficiency (E3)
Committee, Standby Power – Current Status. 2006.. Additionally, the dataset contains blocks of zero data which appear to
be periods without data recording (for example, immediately after meter connection).
6
The NMI is a unique identifier assigned to each electricity connection point within the Australian National Electricity Market
This is a pre-print of the published article Roberts, M.B., N. Haghdadi, A. Bruce and I. MacGill, Characterisation of Australian apartment
electricity demand and its implications for low-carbon cities. Energy, 2019. 180: p. 242-257.
DOI: 10.1016/j.energy.2019.04.222
and so has been used for the first part of this study (sections 4, 5 and 6.3). However, as this group has no
associated demographic or household survey information, all three groups were used in the exploration of
household characteristics (section 6.4). This larger dataset comprises 6034 households, of which 2081 are
apartments or units. Of these, customers from 220 units and 1150 houses participated in a survey, providing
information regarding household demographics, dwelling characteristics and energy and appliance usage.
3.3 Data preparation
Prior to analysis of the load data, missing data was filled to ensure an equal number (17520) of general load
readings for each customer. Following the method used in the CSIRO-Energex report [50], the timestamp with
missing data (tmissing) for a given customer c was compared to all other timestamps in the period to find the ‘most
similar’ timestamp (tsimilar), and the load data copied from the ‘most similar timestamp’ to the missing timestamp
. Similarity between two timestamps is defined by Equation(1) and found by calculating
the sum across the whole dataset of the square of the difference between the load data for the two timestamps.
For customers with missing data at the ‘most similar’ timestamp, the second most similar timestamp was used,
and so-on. As all customers have some general electricity load, this method was used to fill all missing general
load data.
Equation(1)
Of the 6034 households, 3531 have interval data for a controlled load (commonly hot water heating) in addition
to metered general load. Although this controlled load was excluded from the exploration of load variability and
daily profiles, it was included in calculations of total energy use (Section 4.1). Because the controlled load is
inherently intermittent and time-specific, gaps in this part of the dataset were only filled for timestamps with a
simultaneous gap in the general load data, and the ‘most similar’ timestamp for controlled load was constrained
to the same time of day as the timestamp for the missing data. Finally, the annual load profiles were normalised,
using the 99th percentile of the data to ensure robustness against outliers. The processed dataset, along with
household characteristics and the results of the cluster analysis will be made publicly available.
4. Average Daily Energy
4.1 Average total daily energy use
Using the total (general + controlled) load for each customer, daily average loads were calculated for the whole
dataset, divided into ‘units’ and ‘not units’. Figure 1(a) shows that average median household loads are twice as
large (17.7 kWh/day compared to 8.9 kWh/day) for detached and semi-detached houses as for units. This is in
part due to the relatively low occupancy rates of apartments compared to houses, averaging 1.9 compared to
2.7 [9].
As shown by the frequency distribution of average daily energy per occupant, plotted for the smaller surveyed
dataset (Figure 1(b)), the median daily load per occupant for houses is 7.16 kWh while that for units is 21% lower
at 5.69 kWh. In order to assess the significance of the difference in these values, a statistical t-test was applied
to the two distributions. Figure 1 suggests it is at least possible that the two distributions have different
variances, so Welch’s (unequal variance) t-test [74, 75] was applied instead of the more common Student’s t-
test. This gave a p-value of 0.000005% which allows rejection of the null hypothesis that the two distributions
have equal averages and confirms that the average daily household load, normalised for occupants, is
significantly higher for houses than for units, while the greater difference in summer (29%) compared to winter
(21%) is indicative of greater cooling loads in houses.
This is a pre-print of the published article Roberts, M.B., N. Haghdadi, A. Bruce and I. MacGill, Characterisation of Australian apartment
electricity demand and its implications for low-carbon cities. Energy, 2019. 180: p. 242-257.
DOI: 10.1016/j.energy.2019.04.222
(a)
(b)
(c)
Figure 1 - Frequency distribution of (a) average daily total load, (b) average daily load normalised for occupants
and (c) average time of daily peak
4.2 Average daily load profiles
Figure 2 shows the normalised average daily load profile for units and for houses. Compared to houses, units
show a smaller evening peak, particularly in summer. The frequency distributions for the peak load time (Figure
1(c)) show a higher proportion of units have their daily peak in the morning; consequently, the mean peak time
period is earlier for units (17:00) than for houses (17:30), with a broader distribution (standard deviation is 5.3
for units, 4.1 for houses).
In all seasons, average unit daytime loads are flatter than houses (see also Section 5.2), suggesting potentially
greater suitability for PV self-consumption.
5. Variability and load aggregation
5.1 Variability metrics
It is useful to understand the diurnal and annual variability of load profiles for the calculation of network capacity
requirements, load management, suitability assessment for PV and design of appropriately sized storage. A
range of metrics were used to measure variability as a means of comparing general loads of apartments to those
Figure 2 – Normalised average daily general load profiles for houses and units in control group
This is a pre-print of the published article Roberts, M.B., N. Haghdadi, A. Bruce and I. MacGill, Characterisation of Australian apartment
electricity demand and its implications for low-carbon cities. Energy, 2019. 180: p. 242-257.
DOI: 10.1016/j.energy.2019.04.222
of houses (controlled loads were omitted as their time specificity would distort the results), and to explore the
effects of load aggregation.
The average coefficient of variation (CV) is the ratio of the standard deviation of the daily load to its mean, as
shown in Equation(2), where Ed,j is the jth 30-minute energy reading on day d.
Equation(2)
The load factor (LF), a useful metric for appropriately sizing storage capacity, is the mean energy divided by the
peak energy and can be calculated on a daily or annual basis as shown in Equation(3) and Equation(4).
Equation(3)
Equation(4)
Because of the disparity between electricity tariffs for imported and exported energy, the potential for PV self-
consumption is a factor to consider in assessing the suitability of different loads to utilisation of on-site PV
generation. A range of parameters can be found in the literature [76-78] for measuring PV self-consumption but,
in essence, this metric refers to the amount or proportion of on-site PV generation that is consumed by a load,
and therefore depends on the size, orientation and output characteristics of the PV system, as well as the
weather conditions during the period under consideration, and the size and shape of the load profile.
For the purposes of this study, we propose two alternative PV self-consumption metrics (SCMs) that are
independent of both the size of the load and the PV system size, measuring the degree to which the shape of an
annual load profile matches the shape of the generation profile of an optimally orientated, co-located PV system
over the same period. They are given by Equation(5) and Equation(6) where p =
(
is the normalised
PV generation and e = (
is the normalised load for timestamps t = 1,2, ...T. The PV profiles were
generated using NREL’s System Advisor Model (SAM) [79] with weather files for 2013 generated from the
Australian Bureau of Meteorology (BOM) gridded satellite insolation data [80] and temperature and wind speed
from the BOM automatic weather stations (AWS).
7
Equation(5)
Equation(6)
5.2 Variability results
Figure 3 shows the distribution of the variability metrics discussed above for houses and for units, with average
values shown in Table 1. Welch’s t-test, applied to the distributions of each metric, all returned p-values below
0.0003%, showing a high degree of certainty that the variabilities of the house and unit loads are significantly
different on all these metrics.
7
As the exact locations of the SGSC customers are not known, weather files were generated using data for the geographical
centre of the postcode area for each customer.
This is a pre-print of the published article Roberts, M.B., N. Haghdadi, A. Bruce and I. MacGill, Characterisation of Australian apartment
electricity demand and its implications for low-carbon cities. Energy, 2019. 180: p. 242-257.
DOI: 10.1016/j.energy.2019.04.222
( a) Coefficient of variation
( b) Daily load factor
( c) Annual load factor
(d) PV Self-consumption SCM1
(e) PV Self-consumption SCM2
Figure 3 - Frequency distribution of variability and self-consumption metrics
On average, individual unit load profiles show higher coefficient of variation and lower load factor (whether
calculated on a daily or an annual basis) than load profiles for houses. This greater temporal variability in average
unit loads may be related to the lower proportion of households with children, and therefore lower daytime
energy use. Alternatively, lower variability in houses may be due to the smoothing effect of higher occupancy.
Additionally, Figure 3 shows that apartment households have a broader distribution of temporal variability
between customers.
For all dwelling types, mean load factor calculated on an average daily basis is lower in winter than summer (by
9% for units and 12% for houses), while mean coefficient of variation is higher in winter (15% for units, 20% for
houses). This suggests that, on the hot summer days when it is used, air conditioning is used for longer duration
compared to winter electric heating use (so that days with high peak cooling loads also have high mean loads,
whilst high heating peak loads have less impact on the daily mean load) and may be related to households with
gas heating and either sparingly-used supplementary electric heating or electric ovens (common even where
cooktops are gas). Conversely, load factor calculated across the whole season is lowest in spring / autumn when
there are less extreme heating or cooling loads, and is higher in winter than summer (by 7% and 9% for units
and houses respectively), as a single summer peak day can disproportionately lower the seasonal value. In all
seasons, average weekend loads show slightly earlier peak time, higher load factor and lower coefficient of
variability than weekday loads for all dwelling types, due to higher levels of daytime occupancy.
Table 1 Average variability metrics for household loads
Unit Load Profiles
House Load Profiles
Welch’s t-test
Mean
Median
Std Dev
Mean
Median
Std Dev
t
P
Coefficient of Variation
1.05
0.98
0.38
0.82
0.80
0.26
24.9
9.8 x 10-125
Average Daily Load Factor
0.26
0.25
0.09
0.31
0.31
0.08
-22.7
7.8 x 10-107
Annual Load Factor
0.08
0.08
0.04
0.11
0.10
0.04
-26.1
1.2 x 10-140
Average Daily Peak Time
17:00
18:30
5.3
17:30
18:30
4.1
Self-Consumption SCM1 (%)
31.7
30.8
6.6
30.9
30.6
5.8
4.7
3.4 x 10-6
Self-Consumption SCM2 (%)
31.1
31.1
5.0
32.9
32.9
5.4
-13.0
4.9 x 10-38
Although the t-test indicates a significant difference in the average self-consumption for houses and units, the
values are close with houses or units having the greater value depending on the metric chosen.
This is a pre-print of the published article Roberts, M.B., N. Haghdadi, A. Bruce and I. MacGill, Characterisation of Australian apartment
electricity demand and its implications for low-carbon cities. Energy, 2019. 180: p. 242-257.
DOI: 10.1016/j.energy.2019.04.222
5.3 Load aggregation
For each of the datasets (‘units’ and ‘not units’) annual load profiles were selected at random from the whole
dataset and combined to create aggregations of between two and 250 households, and variability metrics were
calculated for the aggregated load. This process was repeated 100 or 200 times for each size of aggregation and
the average of each metric was calculated. Figure 4(a) to (c) show that, for all these metrics, load variability is
reduced by aggregation of up to 50 household loads. The higher coefficient of variation and lower daily load
factor of unit loads compared to house loads is apparent in aggregations of 50 or below, but above this, these
metrics do not distinguish between house loads and unit loads. However, annual load factor for large
aggregations of unit loads is 35% compared to aggregated house loads of 30%, due to the higher likelihood of
outlier peak cooling loads in large houses.
On the first metric, self-consumption is not affected by aggregation of household loads, while on the second,
there is a significant increase but only for small groups. Using either metric, self-consumption calculated solely
on the shape of the aggregate profile is not affected by aggregation above ten households (Figure 4(e) and (f)).
The coincidence factor of a collection of loads can be defined as the ratio of the system or aggregate peak to the
sum of the individual, non-co-incident peaks, as shown in Equation (7). This metric has relevance in the
calculation of potential demand charge components in retail tariffs, and more generally in assessing network
impacts.
(a) Coefficient of variation
(b) Daily load factor
(c) Annual load factor
(d) Coincidence factor
(e) PV Self-consumption, SC1
(f) PV Self-consumption, SC2
Figure 4 - Variability metrics for aggregated loads
As shown in Figure 4(d), the coincidence factor for unit load profiles tends towards 0.23 for aggregations over
200 customers, while for houses the figure is 0.37. This suggests relatively large benefits in aggregating unit
loads (for example in an embedded network) in terms of reduced demand charges and network impacts.
Equation (7)
6. Clustering and classification
6.1 Clustering method
In order to explore the range of load profiles for different customers in different dwellings, a cluster analysis was
firstly carried out for all the dwellings (‘units’ and ‘not units’) in the control group only (1786 households), as
this is the group most representative of the wider population. This dataset (labelled ca) was divided into clusters
of similarly-shaped profiles, irrespective of dwelling type or other household characteristics.
This is a pre-print of the published article Roberts, M.B., N. Haghdadi, A. Bruce and I. MacGill, Characterisation of Australian apartment
electricity demand and its implications for low-carbon cities. Energy, 2019. 180: p. 242-257.
DOI: 10.1016/j.energy.2019.04.222
Because there are 17520 features (30-minute timestamps) for each household, the dataset is too sparse to
cluster without first reducing the number of features. In order to retain information regarding diurnal and
seasonal variability, the profiles were first grouped by month and by the type of day (weekday or weekend),
reducing the features to 1125 (number of months x number of day types x number of readings per day = 12 x 2
x 48). Principle component analysis (PCA) was then applied to further reduce the number of features, whilst
minimising the loss of useful data. A final figure of 180 features was chosen as optimal for greatly increased
computation with only 10% loss of data (see Figure 5).
Figure 5- Optimisation of number of features through PCA
Figure 6 - SUM validity index versus number of clusters
The dataset was then clustered using k-means clustering to partition the whole dataset into up to 40 clusters.
The SUM validity index was used to assess the similarity between and within clusters. From Figure 6, it can be
seen that increasing the number of clusters above ten gives minimal variation in the index, suggesting ten
clusters are sufficient to capture the variability of the dataset.
As the demographic and household data available for the control group is extremely limited (consisting only of
assumed values for dwelling type, household income, electricity use and gas use, as well as the climate zone and
geographical region of the dwelling), further clustering was carried out, again using 10 profile classes, for the
2000 units (apartments) in all 3 data groups (the control group, those that were offered but declined demand
management products, and those that accepted only home energy monitors - see Section 3.2), dataset 3u.
6.2 Classification method
A classification process was used to explore the relationship between the profile classes and a mixture of
assumed and known household characteristics
8
(for the control group), with additional household survey data
9
(for the larger dataset). Prior to classification, each of the datasets (ca and 3u) was randomly divided into a
learning set containing 80% of the customers and a testing set containing the remaining 20%.
In order to examine the dependence of membership of each profile class on customer demographics and
household characteristics, a multinomial logistic regression (MLR) was applied to the data. Given J profile classes
, the probability of a household with n explanatory variables (given by
=
belonging
to profile class j is and the “logit” or log odds ratio” relative to a reference class
J is given by Equation(8) [81].
where
Equation(8)
The coefficients were calculated from fitting an MLR to the training data, using an iterative Maximum
Likelihood method implemented in Python through sci-kit learn [82] with one-versus-rest and multi-class training
algorithms, and sag and saga solvers [83]. The coefficients were then applied to the test data to predict the
profile classes of each customer. Accuracy scores (the proportion of customers allocated to the correct profile
8
The data fields for the control group are TRIAL_REGION_NAME, POSTCODE, LOCAL_GOV_AREA_NAME, SUBURB_NAME,
LOCATION_TYPE_CD, SERVICE_TYPE, GENERAL_SUPPLY_CNT, CONTROLLED_LOAD_CNT, NET_SOLAR_CNT, GROSS_SOLAR_CNT,
OTHER_LOAD_CNT, ASSRTD_HHOLD_INCOME_GROUP_CD, ASSRTD_CLIMATE_ZONE_CD, ASSRTD_CLIMATE_ZONE_DESC,
ASSRTD_DWELLING_TYPE_CD, ASSRTD_GAS_USAGE_GROUP_CD, ASSRTD_ELECTRICITY_USE_GRP_CD.
9
The additional data fields from the household survey are DWELLING_TYPE_CD, HHOLD_INCOME_GROUP_CD, DRYER_USAGE_CD,
REDUCING_CONSUMPTION_CD, AIRCON_TYPE_CD, NUM_OCCUPANTS, NUM_CHILDREN_0_10, NUM_CHILDREN_11_17,
NUM_OCCUPANTS_70PLUS, HAS_CHILDREN, NUM_REFRIGERATORS, NUM_ROOMS_HEATED, HAS_GENERATION, HAS_INTERNET_ACCESS,
HAS_GAS, HAS_GAS_HEATING, HAS_GAS_HOT_WATER, HAS_GAS_COOKING, HAS_SOLAR, HAS_POOLPUMP, HAS_AIRCON, IS_RENTING,
HAS_GAS_OTHER_APPLIANCE, IS_HOME_DURING_DAYTIME.
This is a pre-print of the published article Roberts, M.B., N. Haghdadi, A. Bruce and I. MacGill, Characterisation of Australian apartment
electricity demand and its implications for low-carbon cities. Energy, 2019. 180: p. 242-257.
DOI: 10.1016/j.energy.2019.04.222
class) were calculated for the training data and for the test data to determine the optimum number of features
to use in the regression.
Before fitting the MLR, the available features were first converted to binary variables by creating ‘dummy’
variables relative to a base variable which was removed from the list. For the non-surveyed control group (ca),
the features were further reduced by removing those with a very low variance (HAS_GROSS_SOLAR ) or those
likely to have a high degree of co-linearity with retained features (TRIAL_REGION_NAME, HAS_GROSS_SOLAR
and ASSRTD_ELECTRICITY_USE), leaving the final list of variables shown in Table 2 below.
For the remaining dataset (3u), which includes surveyed customers, a process of feature selection was applied
in order to reduce the likelihood of overfitting due to the large number of features in the household survey data.
After removing variables with over 90% homogeneity (‘HAS_SOLAR’, ‘LOCATION_TYPE’, ‘HAS’GENERATION’,
’HAS_GROSS_SOLAR’, ‘HAS_INTERNET_ACCESS’) and the ‘assumed’ and ‘assigned’ variables (which are likely to
have a high level of co-linearity with the equivalent surveyed variables), recursive feature elimination (RFE) was
applied to progressively eliminate the least important remaining variables. At each stage, an iterative MLR
process was applied to the features and training and test scores were recorded in order to determine the
optimum number of features.
6.3 Control group, all dwellings (ca)
Figure 7 shows the average profile for each of the 10 profile classes (PCs) for all dwelling types in the control
group (1786 customers). PCs ca9, ca1, and ca3 (shown in blue) have a higher proportion of houses than units
while PC ca10 and ca2 and (to a lesser extent) PC ca4 (all shown in red), have a higher proportion of units. Table
2 shows some characteristics of the PCs. Those with more units include the cluster with the lowest overall energy
use and are seen to have more pronounced peaks (morning and evening) in winter than summer, suggesting
greater use of heating or electric cooking – but for shorter periods - than summer air conditioning in apartments.
The PCs with more houses than units include PC ca9 with flat daytime load all year (suggesting high air
conditioning and heating use, with residents home during the daytime), PC ca3 with high summer daytime load
but lower in winter (possibly due to high air conditioning use in households with gas or non-existent heating),
as well as PC ca1 with high overnight load in both winter and summer.
A multinomial logistic regression was carried out using the assumed characteristics of the control group
household as explanatory variables and the MLR coefficients obtained are shown in Table 2. The highest
coefficients are for ASSRTD_DWELLING_TYPE_CD_Unit showing a strong positive correlation with PCs ca10, ca2
and ca4, as expected, some negative correlation with ca9 and only weak or negligible negative correlation with
ca1 and ca3. Bearing in mind that the clustered profiles exclude controlled loads (nearly all overnight water
heating), the strong negative correlation between HAS_CONTROLLED_LOAD and the flat profile of PC ca10 may
be because these households have non-off-peak electric water heating, while the positive correlation with ca4
(with high evening peaks) may be because these households with controlled (likely water heating) load are less
likely to have gas and therefore more likely to use electricity for cooking. The regression gave a relatively low
training score of 0.22 and a test score of 0.20. It is unsurprising that these assumed variables alone are
inadequate to reliably predict the shape of a customers’ annual load profile, but the score is twice that expected
from chance for ten PCs.
This is a pre-print of the published article Roberts, M.B., N. Haghdadi, A. Bruce and I. MacGill, Characterisation of Australian apartment
electricity demand and its implications for low-carbon cities. Energy, 2019. 180: p. 242-257.
DOI: 10.1016/j.energy.2019.04.222
Figure 7 – Average cluster profiles (ca1 to ca10) for all dwellings in control group
Table 2 Profile classes and classification coefficients for control group, all dwellings (ca)
MLR Coefficients
Cluster (ca)
Cluster Size
Units as % of cluster
Average daily Etot (kWh)
(Summer / Winter)
ASSRTD_DWELLING_
TYPE_CD_Unit
HAS_CONTROLLED_LOAD
ASSRTD_HHOLD_INCOME
_GROUP_CD_LOW
ASSRTD_GAS_USAGE_
GROUP_CD_LOW
ASSRTD_CLIMATE_ZONE
_DESC_Mild temperate
ASSRTD_GAS_USAGE
_GROUP_CD_HI
ASSRTD_HHOLD
_INCOME_GROUP_CD_HI
ca1
106
20.8
18.4 / 22.9
0.00
-0.08
-0.33
0.24
0.00
0.01
0.00
ca2
199
50.3
12.8 / 17.5
0.89
0.00
0.67
0.00
0.22
-0.11
-0.08
ca3
211
21.3
20.0 / 19.1
-0.10
0.00
-0.05
-0.11
-0.11
0.00
0.14
ca4
258
34.9
11.1 / 17.6
0.84
0.58
-0.04
-0.47
-0.39
0.00
-0.01
ca5
130
27.7
13.5 / 31.9
0.00
0.00
0.00
0.26
0.18
-0.06
-0.24
ca6
289
22.8
15.0 / 20.5
0.06
0.00
-0.26
-0.07
-0.26
0.10
0.16
ca7
171
22.2
19.3 / 13.4
-0.07
0.14
0.00
0.04
-0.23
-0.64
0.00
ca8
190
22.6
19.4 / 22.3
-0.11
0.00
0.08
-0.05
0.00
0.35
0.00
ca9
132
20.5
18.6 / 19.1
-0.34
0.00
0.09
0.00
0.10
0.00
-0.30
ca10
100
59.0
8.0 / 10.9
0.95
-0.82
0.28
0.46
0.29
0.10
0.10
Max absolute
0.95
0.82
0.67
0.47
0.39
0.64
0.30
Mean absolute
0.39
0.25
0.23
0.22
0.21
0.20
0.12
6.4 Household characteristics of apartments (3u)
In order to better examine the range of load profiles exhibited by apartment households, the apartments from
the larger dataset were clustered independently into ten clusters. Figure 8 shows the average daily profiles for
these classes, while Table 3 shows the distribution of unit profiles between the clusters and selected household
and demographic information. It should be noted that, although clustering was applied to load profiles for 2081
units, survey data was only available for 225 of these customers, including an atypically low proportion of renters
(seven, compared to a national average of 60% of apartment residents [9]).
This is a pre-print of the published article Roberts, M.B., N. Haghdadi, A. Bruce and I. MacGill, Characterisation of Australian apartment
electricity demand and its implications for low-carbon cities. Energy, 2019. 180: p. 242-257.
DOI: 10.1016/j.energy.2019.04.222
Figure 8 - Average profiles for 10 clusters of units from 3 customer groups
Table 3 Household characteristics of profile classes for 3u
Cluster (3u)
% of Dataset
Average daily total
energy (kWh)
(summer / winter)
Mean time period
of peak
Average Occupancy
% with residents
over 70
% with children
Average Income
1=low, 2=med, 3=high
% with aircon
% with Gas
% with gas hot water
% with gas cooking
% with gas heating
% renting
3u1
13%
6.9 / 13.1
18:30
1.7
46%
9%
2.3
49%
49%
23%
40%
14%
0%
3u2
12%
9.3 / 9.7
18:30
2.0
4%
16%
2.4
20%
72%
36%
68%
20%
12%
3u3
4%
12.0 / 13.0
18:00
1.7
27%
0%
1.5
9%
82%
55%
73%
9%
9%
3u4
12%
10.9 / 15.3
14:00
1.3
33%
10%
1.7
36%
36%
23%
27%
5%
0%
3u5
16%
9.1 / 9.7
19:30
1.8
3%
9%
2.7
28%
87%
31%
69%
38%
0%
3u6
6%
9.3 / 21.6
16:00
2.0
0%
0%
2.2
33%
67%
44%
67%
22%
11%
3u7
11%
10.0 / 11.8
17:30
1.6
57%
3%
1.5
63%
40%
33%
20%
13%
0%
3u8
11%
8.0 / 10.8
10:30
1.5
34%
9%
1.6
26%
11%
6%
6%
3%
2%
3u9
5%
14.3 / 7.3
18:30
2.6
11%
0%
2.4
67%
78%
33%
67%
11%
11%
3u10
9%
7.4 / 12.7
19:00
1.8
22%
20%
1.8
50%
60%
20%
30%
0%
0%
Figure 9 shows the average MLR accuracy scores achieved as recursive feature elimination was applied to the
survey data for these units. The low test score compared to training scores, even for a low number of features,
suggests that the regression model is overfitting to the small, sparse dataset. However, some characteristics of
the profile classes can be deduced from their shapes and from the data presented Table 3.
This is a pre-print of the published article Roberts, M.B., N. Haghdadi, A. Bruce and I. MacGill, Characterisation of Australian apartment
electricity demand and its implications for low-carbon cities. Energy, 2019. 180: p. 242-257.
DOI: 10.1016/j.energy.2019.04.222
Figure 9 – Accuracy scores vs number of explanatory variables for dataset 3u
Almost half of the households in 3u1 have residents over 70, and this is reflected by flat profiles except for high
evening heating peaks in winter. 3u2 is also flat, with low evening peaks and similar loads summer and winter,
likely due to the high proportion of households with gas, particularly used for cooking. The smallest class, 3u3,
has a moderately high 24-hour load with a low early-evening peak. 3u4 has high, flat daytime load, particularly
in winter, with very low peaks, having a low % of households with gas heating. Households in 3u5 and 3u6
contain relatively affluent couples with a low proportion of children and aged people. In 3u5, this is reflected by
the later evening peak, while 3u6 households have very high overnight heating loads in winter, resulting in a
very early average peak time. Over half the households in 3u7 contain elderly residents and their profiles show
an early evening peak that is more pronounced and narrower in winter. 3u8 is the only class with a morning
peak, which is most pronounced in winter and may be explained by the very low incidence of gas heating. 3u9
has the largest average households, though without children, and is the only class to have higher summer loads
than winter, while the high proportion of households having gas cooking makes the profile relatively flat. Finally,
3u10 has relatively flat profiles in summer but high overnight heating loads in winter.
7. Discussion and conclusions
Excluding common property loads, the average electricity demand per occupant is lower for apartment residents
than for houses, although, because of the absence of data on the size of the dwellings in the study, it is not clear
whether this is simply due to the typically smaller floor area of apartments or to other features such as shared
walls (hence improved thermal performance) or lower levels of appliance ownership or use. It would be useful
in future studies to collect more physical data pertaining to the dwellings, including floor area and number and
orientation of external walls.
Although the average daily profile of all the apartments is flatter than that for houses, the diurnal variability of
individual apartment loads is, on average, higher than that for houses. Their wider distribution of peak time and
of daily variability also suggests greater diversity between apartment load profiles than between those of
houses. For all dwelling types, aggregating loads in groups of up to 50 households increases load factor and
reduces variability, but this effect is more pronounced for apartments due to the greater diversity of their load
profiles. While dwelling type makes no discernible difference to daily load variability for larger aggregations of
households, load factor calculated on an annual basis is higher for aggregated apartment loads than for houses,
and the coincidence factor of aggregated apartment loads is lower.
Based solely on the shape of the load profile, aggregation in groups of up to ten households may increase self-
consumption of PV, but, perhaps surprisingly, no further benefit is shown for larger aggregations.
Although the study does not reveal distinct apartment or house load profiles, the application of cluster analysis
to annual load profiles does show that there are groups of profiles that are more likely to belong to apartment
households and those more likely to be from houses. Indeed, dwelling type is shown to be one of the more
important indicators of load profile, along with elderly occupants or having a gas cooker or a pool pump.
Although the SGSC dataset has a high incidence of apartments, both proportionally and in absolute quantity,
compared with other published studies, the significance of the classification analysis is affected by the low
number of apartment residents who participated in the household survey, although it is possible that more
complex classification methods (such as ensemble decision tree or support vector machine), or the use of k-fold
cross-validation would yield more conclusive results. A larger dataset, with household survey data for all
apartments, would enable a more detailed analysis of the relationship between load profiles and household
characteristics and could usefully facilitate an examination of the effects on load shape and variability of
This is a pre-print of the published article Roberts, M.B., N. Haghdadi, A. Bruce and I. MacGill, Characterisation of Australian apartment
electricity demand and its implications for low-carbon cities. Energy, 2019. 180: p. 242-257.
DOI: 10.1016/j.energy.2019.04.222
aggregating loads within and between clusters to explore the benefits of household diversity on aggregated
loads. The potential applications of this research include design of distributed PV and battery storage for
apartment buildings and distribution network planning, whether installation of new infrastructure for greenfield
residential developments or augmentation of existing assets in urban areas where housing density is increasing.
More generally, our findings highlight some of the opportunities as well as challenges that a focus on higher
density urban form through apartment living pose for future low-carbon cities.
Acknowledgements
This research is supported by a project grant (AP841) from Energy Consumers Australia. The lead author
gratefully acknowledges the support of a Research Training Program Stipend from the Australian Government
and of a scholarship funded by the CRC for Low Carbon Living. The authors would like to thank Dr Tess Stafford
for her insights on the SGSC dataset.
Declarations of Interest: None.
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