Applied Energy 87 (2010) 1880–1892

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Applied Energy

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A high-resolution stochastic model of domestic activity patternsand electricity demand

Joakim Widén *, Ewa WäckelgårdDepartment of Engineering Sciences, The Ångström Laboratory, Uppsala University, P.O. Box 534, SE-751 21 Uppsala, Sweden

a r t i c l e i n f o a b s t r a c t

Article history:Received 20 May 2009Received in revised form 2 September 2009Accepted 4 November 2009Available online 28 November 2009

Keywords:Domestic electricity demandStochasticMarkov chainBottom-upLoad model

0306-2619/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.apenergy.2009.11.006

* Corresponding author. Tel.: +46 18 471 37 82; faxE-mail address: joakim.widen@angstrom.uu.se (J.

Realistic time-resolved data on occupant behaviour, presence and energy use are important inputs to var-ious types of simulations, including performance of small-scale energy systems and buildings’ indoor cli-mate, use of lighting and energy demand. This paper presents a modelling framework for stochasticgeneration of high-resolution series of such data. The model generates both synthetic activity sequencesof individual household members, including occupancy states, and domestic electricity demand based onthese patterns. The activity-generating model, based on non-homogeneous Markov chains that are tunedto an extensive empirical time-use data set, creates a realistic spread of activities over time, down to a1-min resolution. A detailed validation against measurements shows that modelled power demand datafor individual households as well as aggregate demand for an arbitrary number of households are highlyrealistic in terms of end-use composition, annual and diurnal variations, diversity between households,short time-scale fluctuations and load coincidence. An important aim with the model development hasbeen to maintain a sound balance between complexity and output quality. Although the model yieldsa high-quality output, the proposed model structure is uncomplicated in comparison to other availabledomestic load models.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Energy efficiency measures and application of emergent renew-able energy technologies have made the energy end-user increas-ingly important and influential on system operation. Oneexample is distributed electricity generation in low-voltage grids,where the impact of widespread on-site generation on networkvoltages is influenced by the matching with domestic electricitydemand [1,2]. Another example is performance of solar heatingsystems, which are influenced by domestic hot water load profiles[3,4]. Occupant presence and behaviour are likely to become moreinfluential on the heat balance in buildings as low-energy architec-ture is introduced, since this is more sensitive to body heat andexcess heat from appliances [5]. Application of demand side man-agement schemes and load shifting strategies that actively seek totransform the energy demand of the end-user calls for improvedknowledge and modelling of what end-users actually do. For anal-yses and simulations, there is a need of improved, detailed modelsof occupant behaviour and energy use in buildings.

Modelling of domestic electricity demand for studies of on-sitedistributed generation in a large number of individual households,which is the subject of this paper, is a complex task. In a realistic

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: +46 18 50 01 31.Widén).

reproduction the stochastic behaviour of the demand must be cap-tured; more specifically in terms of variations between households,spread of demand levels for different end-uses over time, varia-tions over seasons and days, differences between weekdays andweekend days and load coincidence.

To break down the problem, electricity use in a single house-hold depends on three factors: (a) the set of appliances in thehousehold, (b) the individual electricity demand of these appli-ances, and (c) the use of the appliances. With perfect knowledgeof these factors, the electricity use in a household can be deter-mined. The most complex and unpredictable of these is withoutdoubt the behavioural factor (c).

Bottom-up models, of which the Capasso model [6] is the mostcommonly cited example, combine detailed data on the factors(a)–(c) to determine the electricity demand of an arbitrary numberof households. A similar bottom-up approach is used by Paateroand Lund [7]. In general, these models and other high-resolutiondemand models, such as the model by Stokes [8], tend to be com-plex and dependent on large amounts of input data and assump-tions. The challenge with detailed demand modelling musttherefore be to keep the model structure as simple as possiblewhile ensuring sufficiently realistic output data. In particular, thereis a need for an efficient but realistic treatment of the behaviouralfactor, as this determines stochastic fluctuations and end-use com-position over time.

J. Widén, E. Wäckelgård / Applied Energy 87 (2010) 1880–1892 1881

In a previous paper we showed that time-use (TU) data—sequential high-resolution data on daily activities of householdmembers, usually collected through diaries—can be used for highlyrealistic descriptions of the behavioural factor (c) [9]. TU data weresubsequently used to describe occupancy patterns in a stochasticMarkov chain based model of domestic lighting demand [10]. Sim-ilar efforts have also been made by Page et al. [11] and Richardsonet al. [12,13]. Both Stokes and Richardson et al. suggest further useof occupancy profiles in demand modelling to make modelled datadepend on the availability of occupants [8,12]. Already, occupancypatterns form the basis of models for ventilation [14] and officelighting [15]. Another approach with an even more realistic ba-sis—if the TU data are detailed enough to allow it—is to extendoccupancy modelling to modelling of synthetic multiple-activityprofiles.

In this paper the approach in Ref. [10] is extended to a high-res-olution stochastic model of multiple electricity-dependent activi-ties in households and the associated electricity demand, basedon a simplistic description of factors (a) and (b) from appliance-specific measurements in households, and a realistic Markov-chainmodel of factor (c) based on TU data. The stochastic Markov-chainprocess, which discriminates between weekdays and weekenddays and between detached houses and apartments, generateshigh-resolved synthetic activity sequences to which applianceloads are connected to create power demand data for a variety ofend-uses.

The aim has been to keep the required input data at a minimumand the model structure as simple as possible, while keeping themodel output highly realistic. At present, the model is limited tohousehold electricity (i.e. excluding heating and maintenance elec-tricity), but the general model structure is easily extended andapplicable, e.g. to heating and domestic hot water (DHW). Routinesfor generating DHW profiles from empirical TU data have already

00:001

9

Activ

ity

00:001

9

Activ

ity

00:001

9

Activ

ity

Generation of synthetic activity patterns for each household member.

k = time step i = household member

Conversion to household power demand.

k = time step j = end-use category

A(k,i)

P(k,j)

Markov-chain

transition probabilities

Appliance load

parameters

L(k)

0

1

2

3

Pow

er (k

W)

(a) Model overview (b) Ex

Fig. 1. Outline of the model. (a) shows the two main steps involved in the generation of adata LðkÞ. (b) shows example activity profiles for a 3-person household and resulting pothose listed in Tables 1 and 2.

been developed [9] and can be applied to synthetic activity pat-terns without much modification. The generated activity patternscan also be used to simulate high-resolution occupancy and occu-pant behaviour in various types of building simulations.

In Section 2 the model is described in detail. Section 3 describesthe data used for parameter estimates, input and validation of themodel. In Section 4 the model is validated in terms of aggregate de-mand, stochastic behaviour and load coincidence. In Section 5 themain findings are discussed, as well as possible extensions andapplications of the model. Conclusions are drawn in Section 6.

2. Model framework

To generate power demand data for a household, the modelproceeds in two main steps, as outlined in Fig. 1. Synthetic activitypatterns are generated for each household member in the first stepand these patterns are then converted into power demand for thehousehold in the second step. Input data to the model are daylightdata, converted from solar irradiance, that are fed into the conver-sion model for generation of lighting demand. Parameters are Mar-kov-chain transition probabilities that dictate activity changes forhousehold members, possible to determine from TU data, andhousehold appliance loads, determined from measurements or sta-tistics. This procedure can be repeated for an arbitrary number ofhouseholds to create a larger set of demand data.

2.1. Generation of synthetic activity patterns

2.1.1. Markov-chain modelA model for generation of synthetic occupancy patterns in

households—comprising the three states ’absent’, ’present and ac-tive’ and ’present and inactive’—has been presented in Ref. [10].

12:00 24:00

12:00 24:00

12:00 24:00

12:00 24:00

A(k,1)

A(k,2)

A(k,3)

P(k,2): Lighting P(k,1): Cold appliances

P(k,6): TV P(k,7): computer

P(k,3): cooking

ample output for a 3-person household

Minute time step (k)

Minute time step (k)

ctivity patterns A and power demand P, together with parameters and input daylightwer demand divided on different end-uses. Activities and end-uses correspond to

1882 J. Widén, E. Wäckelgård / Applied Energy 87 (2010) 1880–1892

In the present paper, the occupancy model is extended to include anumber of electricity-dependent activities in the active state.These are chosen such that they can be unambiguously determinedfrom the TU data set that is used. The activities are numbered andshown in Table 1.

Table 1Activities/states in the Markov-chain model.

Activity Description

1 Away2 Sleeping3 Cooking4 Dishwashing5 Washing6 TV7 Computer8 Audio9 Other

k –2 k –1 k k + 1

1

2

3

4

5

6

7

8

9

p2,1 p2,2 p2,3 p2,4 p2,5 p2,6 p2,7 p2,8 p2,9

U ∼ [0,1]

(a) Random generation of state transition in time step k

(b) State transition in time step k

Transition probabilities

Time step

Markov-chainstate

0 1

Fig. 2. Generation of synthetic activity sequences in the Markov-chain model. (a)shows how a uniform random number is used to determine the state change takingplace in (b) between time steps k and kþ 1.

Table 2Summary of model routines in the activity-to-power conversion.

End-use j Model routine Par

Cold appliances 1 Cyclic demand PON

Lighting 2 Daylight-dependent PAB

Cooking 3 Conversion scheme A PON

Dishwashing 4 Conversion scheme B P1;

Washing 5 Conversion scheme B P1;

TV 6 Conversion scheme C PON

Computer 7 Conversion scheme C PON

Stereo 8 Conversion scheme C PON

Additional 9 Constant demand PAD

In the Markov-chain model it is assumed that a person in thehousehold performs one of these activities in every discrete timestep k ¼ 1; . . . ;Nk. When time proceeds from k to kþ 1 there is atransition probability pijðkÞ of going from state i to j. This includesthe probability piiðkÞ of staying in state i.

Diurnal fluctuations in daily activities are reproduced by allow-ing transition probabilities to vary over the day. By definition, theMarkov chain is then non-homogeneous as compared to homoge-neous processes with fixed transition probabilities [16].

Activity patterns are generated from the set of transition prob-abilities as outlined in Fig. 2. In each time step a random uniformnumber is generated and compared to the transition probabilitiesto determine which transition is taking place. Note that in the firsttime step an initial state for the Markov process must be set.

2.1.2. Transition probability estimatesTransition probabilities can be straightforwardly estimated

from TU data. Suppose that a series of TU data for N persons, show-ing which of the nine activities is taking place in every time step, isgiven for time steps k ¼ 1; . . . ;Nk. All N transitions between timesteps k and kþ 1 are examined and the total number nijðkÞ of tran-sitions between states i and j are determined. The total number ofchanges from state i is then niðkÞ ¼

P9j¼1nijðkÞ, and the transition

probability estimate is:

pijðkÞ ¼nijðkÞniðkÞ

ð1Þ

If some states lack transitions from them in any time step, niðkÞwill be zero and the above equation cannot be evaluated. One solu-tion is to calculate average transition probabilities over longer timeintervals:

pijðkÞ ¼Pb

s¼anijðsÞPbs¼aniðsÞ

ð2Þ

where k 2 ½a; b�. Direct assignment of a conjectured value might benecessary if no transitions take place within reasonable averagingintervals.

2.2. Activity-to-power conversion

The nine activities in the Markov-chain model correspond todifferent electricity end-uses. In the conversion model (step 2 inFig. 1), generalised load patterns for these end-uses are connectedto the activities. The approach is the same as in Ref. [9], but theload patterns are more sophisticated. The timing of appliance loadswith respect to the performed activity differs; electricity demandcan take place during the activity, directly after the activity orwithout relation to the activities. Sharing of appliances withinhouseholds is taken into account. In addition, the shape of theduty-cycle patterns vary between appliances, as well as standbyelectricity levels. Details on the modelling of different end-uses fol-

ameters Activities Sharing

, duration curves for DtON ;DtOFF – YesSENT ; PINACTIVE; PMAX ; PMIN ; LLIM ;Q ;DP 1–10 No

3 Yes. . . ; PN ; k1; . . . ; kN 4 Yes. . . ; PN ; k1; . . . ; kN 5 Yes; PSTANDBY 7 Yes; PSTANDBY 8 No; PSTANDBY 9 NoD – No

J. Widén, E. Wäckelgård / Applied Energy 87 (2010) 1880–1892 1883

low below. An overview of the model routines is provided in Table2.

2.2.1. Cold appliancesCold appliances are characterised by a cyclic load resulting from

thermostatic temperature control. Although the cycling frequencycan be assumed to vary during the day, due to more or less fre-quent opening and closing of the appliance, this effect can be ne-glected (cf. [26]). The appliance operation can therefore beassumed unrelated to the activity patterns. The applied modellingscheme is depicted in Fig. 3. To define the load cycle of a cold appli-ance the cycle power PON and the time intervals DtON and DtOFF

have to be defined. To introduce realistic stochastic fluctuations,values for DtON and DtOFF can be randomly generated for each coldappliance cycle using inverse transform sampling from durationcurves determined from measured data.

2.2.2. LightingThe lighting part of the model is treated in detail in a separate

paper [10]. In short, the model converts occupancy patterns tolighting demand, with respect to a daylight level determined fromirradiance data. Every household member is assumed to demand apower PABSENT when in the state ’absent’ and a power PINACTIVE whenin the state ’present and inactive’. When in the state ’present andactive’ the desired lighting level of a household member dependson the daylight level LðkÞ, a limiting daylight level LLIM and maxi-mum and minimum power levels PMAX and PMIN:

X1

0

1

X3 X2 X4

U1

U2

U3

U4

X

Prob( tON > X) Prob( tOFF > X)

Time

PON

0

X1 X2 X3 X4

(b) Generated cyclic load patterns

(a) Random generation of cycle intervals

Power

Fig. 3. Schematic outline of the model routine for cyclic demand of cold appliances.In this example, cycle intervals are randomly generated in (a) from uniformlydistributed numbers U1; . . . ;U4 through inverse transform sampling from thedistribution of interval times DtON and DtOFF . The obtained load pattern is shown in(b).

PACTIVEðkÞ ¼PMIN

LðkÞLLIMþ PMAX 1� LðkÞ

LLIM

� �L 6 LLIM

PMIN L > LLIM

(ð3Þ

The daylight level LðkÞ can be determined from irradiance data,using well-established conversion models, such as Ref. [27], as out-lined in Ref. [10].

To add realism to the generated power demand, the actuallighting level of an active person is successively adjusted by anincremental power DP towards the desired level PACTIVE with a con-stant probability Q in each time step. When a household membergoes to the ’absent’ or ’present and inactive’ states, the actual light-ing demand is adjusted to PABSENT or PINACTIVE directly.

The occupancy states ’absent’ and ’present and inactive’ corre-spond to activities 1 and 2 in this model, while the occupancy state’present and active’ corresponds to activities 3–10. Thus, the modelcan be applied on the synthetic activity data generated by themodel without any adjustments.

2.2.3. CookingCooking as a basic activity can involve numerous appliances

such as microwave ovens, ovens, stoves, kettles, etc. To model thisin detail would require either very detailed activity data coveringthe individual sub-activities involved or assumptions on how oftenduring the main cooking activity different appliances are used. Thisproblem has been addressed previously in Ref. [9]. There it wasfound that a simple but sufficiently accurate solution is to assumea constant power demand during the cooking activity, as depictedin Fig. 4a.

Time

PON

0

(a) Conversion scheme A

Activity

Time

P1

0

Activity k1 kN

Time

PON

0

Activity

PSTANDBY

(c) Conversion scheme C

(b) Conversion scheme B

Power

k2

P2 PN

Power

Power

Fig. 4. The three main activity-to-power conversion schemes in the model. In (a)the power demand is constant during the activity, in (b) a variable duty-cycledemand starts directly after the activity and in (c) the power demand is constantduring the activity, with a standby level during non-use.

1884 J. Widén, E. Wäckelgård / Applied Energy 87 (2010) 1880–1892

2.2.4. Dishwashing and washingDishwashers and washing machines have in common that their

power demand starts after the active use of the appliance has fin-ished. The activities in the generated activity patterns are of thetype ’load and turn on machine’. It is therefore assumed that theduty cycle of the machine starts directly after the activity stops.If the activity should appear again before the duty cycle is finishedthe whole cycle restarts. The power demand typically fluctuatesduring the duty cycle in characteristic patterns for the respectiveappliances. These duty-cycle load curves can be approximated bypiecewise linear functions as described in Fig. 4b.

2.2.5. Entertainment appliancesFor what can collectively be called entertainment appliances,

such as TVs, computers and home stereo systems, the power de-mand can be assumed very close to constant during use. Duringnon-use the appliance could be either turned off completely orset in standby mode. In the applied modelling scheme, whichis a more general form of the scheme in Fig. 4a, a constantstandby power demand is assumed during non-use, as depictedin Fig. 4c.

2.2.6. Additional miscellaneous electricityThe model cannot be expected to cover all household electricity

demand with the specified end-use categories. In Ref. [9] it wasfound that load data converted from TU data captured all theimportant specified end-use categories in appliance-specific mea-surements. However, a significant additional unspecified categorywas left. This category was larger for detached houses than forapartments, probably reflecting both larger share of maintenanceelectricity and more additional appliances. For the aggregate dailyload in Ref. [9], the additional demand is close to constant over theday. The approximation applied in the present model is therefore

Time0

Power

Person 1 Person 2 Combined

Without sharing With sharing

2 × PON

PON

Activities

Fig. 5. Shared use of appliances. When an appliance is shared the power demand isdetermined from the combined pattern. Without sharing each individual activitypattern is converted to power demand, resulting in a higher total demand.

Table 3Data sets used for parameter estimates and validation.

Data set Description Survey period

TU-SCB-1996 Pilot survey of time use (TU) byStatistics Sweden (SCB)

1 weekday and 1 weekend daymember between August and

TU/EL-SEA-2007 Combined survey of time useand electricity use by theSwedish Energy Agency (SEA)

Seven annual and seven montelectricity in 14 households frofour successive days (2 weekddays) in five households in the

EL-SEA-2007 Preliminary electricitymeasurements of householdelectricity on individualappliance level by the SEA

Based on annual and monthlybetween 2005 and 2007

to include additional electricity as a constant power PADD perhousehold member. PADD can be determined from the differencebetween the total modelled demand of the specific categoriesand a desired total demand.

2.2.7. Shared use of appliancesCollective use of appliances is complex and not possible to

determine from time-use data without additional information. Inthe model it is assumed that some appliances are completelyshared while others are always used individually. When an appli-ance is individually used, each household member’s activity pat-tern is converted to power demand. When an appliance isshared, the activity patterns are combined to one and then con-verted, as outlined in Fig. 5. This way, explicit assumptions onthe number of household appliances are avoided. Information onsharing for different end-uses is given in Table 2.

3. Data for parameter estimates and validation

Three data sets were used for estimation of parameters and val-idation of the model. Table 3 gives an overview of these. TU-SCB-1996 is the TU data set used for transition probability estimatesin the Markov-chain model. TU/EL-SEA-2007 contains appliance-specific measurements on which the main parameters in the activ-ity-to-power conversion model are based. This data set was alsoused to validate the total model output for individual households.EL-SEA-2007 is used to validate the aggregate model output for alarge number of households. In addition to these, solar irradiancedata are used for conversion to daylight data in the lighting partof the conversion model. In the following, these data are describedin more detail.

3.1. Time-use data for transition probability estimates

The data set TU-SCB-1996 contains the TU data used for estima-tion of the transition probabilities in the Markov-chain model. Thedata originate from a pilot study of time use by Statistics Sweden(SCB) in 1996. All participating household members aged between10 and 97 years wrote diaries reporting their daily activities on1 weekday and 1 weekend day. Activity types are organised in ahierarchic activity code scheme where activities are defined on dif-ferent levels of abstraction [17]. The result is a detailed TU materialwhere activities can be determined down to a 1-min resolution.The data set has been thoroughly examined for consistency andhas been the subject of a number of preceding studies [18–20].After exclusion of erratic and some problematic data the data setused encompasses 431 persons in 103 detached houses and 66apartments. The distribution of household sizes is shown inTable 4.

Number of participants Data resolution

per householdDecember 1996

431 Persons in 103detached houses and 66apartments

Down to 1-min intervals

hly measurements ofm 2005 to 2007. TU forays and 2 weekend

autumn of 2006

Electricity measurementsfor 14 households. TU forfive households with 13persons

Time-use data on 1-minintervals, electricitymeasurements with 10-min means

measurements 217 households 1-h averages based onmeasurements with 10-min means

Table 4Distribution of household sizes in the TU-SCB-1996 data set.

Household size Detached houses Apartments

1 7 262 39 273 26 44 23 65 6 16 1 27 1 0

Total number of households 103 66Total number of persons 298 133Average number of persons per household 2.89 2.02

Table 6Chosen measurement periods in TU/EL-SEA-2007 data set, with household size andtype of dwelling indicated. All periods are from the summer and autumn of 2006.Household names are the same as in Refs. [10,21].

Household Household size Dwelling Chosen time period

A 1 Apartment September 18–October 15B 1 Apartment October 30–November 26C 2 Detached house June 5–July 2D 2 Apartment June 5–July 2E 2 Detached house September 25–October 22F 2 Apartment June 5–July 2G 3 Detached house June 5–July 2H 3 Detached house October 16–November 12I 3 Detached house June 5–July 2J 3 Apartment September 4–October 1K 3 Apartment June 5–July 2L 4 Apartment June 5–July 2M 5 Detached house September 18–October 15N 6 Detached house October 16–November 12

J. Widén, E. Wäckelgård / Applied Energy 87 (2010) 1880–1892 1885

To make it possible to use the data for transition probabilityestimates, the activity categories were collected in categories re-lated to different end-uses. The result is the list already shown inTable 1. These categories were chosen carefully to cover activitiespossible to determine from the TU data, while at the same timekeeping the number of states as low as possible. The categoryscheme in Ref. [9] served as a basis. Drying laundry was excludedsince an overestimation resulted from assuming standard appli-ances in Ref. [9]. Computer demand was underestimated in thesame study, reflecting lower use of computers in 1996. This hasbeen corrected in the proposed model by including activities thatcan be expected to have been ’computerised’ since 1996, such as’homework’. The TV category includes use of related appliancessuch as DVD and VCR.

Apartments and detached houses were separated, as weekdaysand weekend days are by default, so that separate sets of transitionprobabilities could be estimated for the two types of days anddwellings. Hourly averages were used when calculating transitionprobabilities. This approach was used in Ref. [10] with good re-sults. This means that simulations can be run with shorter timesteps, but that the same transition probabilities are used duringeach hour. Some states lacked transitions despite the relativelylong averaging times. This happens exclusively during night hours,so the transition probability to state 2 was set to one in these cases.For simulations with the Markov-chain model, initial states for theprocess must be set. Activities in the first time step for all personsin the TU-SCB-1996 data set are shown in Table 5. The active states3–9 are unoccupied, which is somewhat unrealistic and is due tounreported activities in the TU data during night-time.

3.2. Appliance measurements for activity-to-power conversion andvalidation

The TU/EL-SEA-2007 data set contains data from a combinedsurvey of time use and electricity demand in Swedish households.Electricity demand was measured between 2005 and 2007 inmonthly or annual periods in 14 households. In five of these house-holds TU data were collected. The survey is extensively reported in[21], where the data were carefully examined for consistency andmeasurement errors. The data set has also been used in studiesof on-site photovoltaic generation [22] and for validation in the

Table 5Distribution of initial activities/states in the Markov-chain model, corresponding tothe first time step in the TU-SCB-1996 data set for weekdays.

State Fraction of persons indetached houses (%)

Fraction of personsin apartments (%)

1 6 52 94 953–9 0 0

preceding model papers [9,10]. The survey is part of a large-scalemeasurement project by the Swedish Energy Agency (SEA) aimedat improving energy-demand statistics of the built environmentin Sweden [23].

Individual appliances in this data set were measured with a 10-min resolution. This makes it possible to determine high-resolu-tion load profiles for individual appliance types to be used in theactivity-to-power conversion model (see next section). Completeload data series in the households are used to test statistical prop-erties of the modelled demand data. For the latter analysis, a periodof 4 weeks was extracted from each household. Whole weeks werechosen, as close in time as possible. The resulting periods areshown together with household sizes and dwelling types in Table6. Appliance-specific measurements were collected in categoriescorresponding to the end-uses in Table 2.

3.3. Data for validation of aggregate load profiles

The data set EL-SEA-2007, also from the SEA’s measurementsurvey [23], contains preliminary aggregate demand for all house-holds with finished measurements in late 2007. These data, in theform of hourly load profiles, specific for detached houses andapartments and for weekdays and weekend days, are used to vali-date the model output for large numbers of households.

3.4. Solar irradiance data

Synthetic irradiance data for Stockholm, Sweden, were gener-ated with the climate data simulator and database Meteonorm6.0 [24]. The data series cover 1 year with a 1-min resolution. Con-version to daylight data was done with models in Refs. [27,28] for asouth-facing, vertically oriented triple-glazing window. These par-ticular window assumptions were also used with good results inthe previously published paper about the lighting part of the model[10]. In a study of houses with more well-defined daylighting con-ditions, the window orientation and glazing could be adjusted.

4. Validation

4.1. Method for validation

The aim with the validation of the model is to (a) check thatsimulations for a large number of households with the sameparameter set applied yield mean aggregate load curves that corre-spond to the aggregate load curves in EL-SEA-2007 and (b) checkthat simulations with this parameter set for fewer households cor-

1886 J. Widén, E. Wäckelgård / Applied Energy 87 (2010) 1880–1892

respond in stochastic terms to measurement data for the small setof households in TU/EL-SEA-2007. One small set of households andone large set of households were generated with the model tomake these comparisons.

4.1.1. Simulation of the large household setIndividual appliance data in the TU/EL-SEA-2007 data set were

examined and representative appliance load profiles for estimationof conversion-model parameters were determined. No strict meth-od was applied; however, for most appliances the load profileswere highly similar. Duration curves for a set of representative coldappliance cycle times were determined for modelling of cold appli-ances. For the lighting model, a set of parameters fitted to the EL-SEA-2007 lighting data determined in Ref. [10] was used. The light-ing model parameters were set to vary between individual house-holds and separate sets were defined for detached houses andapartments. For the other end-uses the same parameters wereused for both household types. The additional power level PADD

was calculated from the difference between estimates of total an-nual demand generated with the model and in EL-SEA-2007. Theresulting parameter set is listed in Table 7. Lighting parametersare shown separately in Table 8.

Aggregate mean load curves were determined from simulationsof 200 detached houses and 200 apartments during one summerand one winter week (5 weekdays and 2 weekend days). House-hold sizes were randomly sampled from the distribution in TU-SCB-1996 (see Table 4). Simulations were run with 1-min time

Table 7Parameter values in the activity-to-power conversion model (except lighting),corresponding to a ’standard’ appliance set. The parameters are special cases of thegeneral formulations listed in Table 2.

Parameter Value

PFRIDGE;ON 50 (W)PFREEZER;ON 80 (W)PCOOKING;ON 1500 (W)PDISHWASHING;1 1944 (W)PDISHWASHING;2 120 (W)PDISHWASHING;3 1920 (W)kDISHWASHING;1 17 (min)kDISHWASHING;2 57 (min)kDISHWASHING;3 73 (min)PWASHING;1 1800 (W)PWASHING;2 150 (W)kWASHING;1 20 (min)kWASHING;2 110 (min)PTV ;ON 100 (W)PTV ;STANDBY 20 (W)PCOMPUTER;ON 100 (W)PCOMPUTER;STANDBY 40 (W)PSTEREO;ON 30 (W)PSTEREO;STANDBY 6 (W)PADD;DETACHED 53 (W/person)PADD;APARTMENT 11 (W/person)

Table 8Parameter values in the lighting part of the activity-to-power conversion model,determined in Ref. [10] to increase fit to measured average load curves. Theproportion of households with a specific parameter value is shown in parentheses.

Parameter Detached houses Apartments

LLIM (lux) 1000 1000PABSENT (W) 0 (60%), 40 (40%) 0 (70%), 40 (30%)PINACTIVE (W) 0 (60%), 40 (40%) 0 (70%), 40 (30%)PMIN (W) 40 (80%), 80 (20%) 40PMAX (W) 160 (60%), 200 (40%) 80 (40%), 120 (60%)Q 0.1 0.1DP (W) 40 40

steps and mean hourly load curves were calculated for weekdaysand weekend days. Initial states in the Markov-chain simulationswere chosen as the states of the first time step in the TU-SCB-1996 set, shown in Table 5. An average of summer and winter loadcurves was calculated to estimate the annual mean load curve.From the modelled and measured load curves, total annual de-mand was estimated by weighting totals for weekdays and week-end days:

Etot ¼ 261�X24

h¼1

PwdðhÞ þ 104�X24

h¼1

PwedðhÞ ð4Þ

where Pwd and Pwed are load curves for weekday and weekend day,respectively.

4.1.2. Simulation of the small household setWhen a realistic aggregate behaviour of the model is assured,

the challenge of the model is to realistically reproduce diversityand time-variability in the demand for fewer households. To deter-mine if this is the case, 14 households were simulated with thesame household sizes and dwelling types as in Table 6. Insolationdata for the exact time periods reported in Table 6 were extractedfrom the annual data series to model daylight level, used as inputto the lighting conversion for the households. The same sequencesof weekdays and weekend days as in the measurement data wereused when generating synthetic activity patterns in the model.

The parameters in Table 7 were applied. Note that this meansthat parameter values are estimated from the same data set thatthe model is validated against. However, the stochastic featuresthat are compared for the small household set do not in any waydepend critically on the conversion parameters, but on the Mar-kov-chain model, which is tuned to the completely separate TU-SCB-1996 data set. The higher lighting parameter values in Table8 were used for all households, as Ref. [10] showed that this gavea reasonable fit to the lighting data of these households. The anal-ysis has to be restricted to specified demand only, because of prob-lems with separating additional household electricity from otheradditional electricity use (mainly heating) in the measured data.

4.1.3. Load curve measuresApart from standard statistical measures such as mean values,

standard deviation, maxima and minima, the shape of a load curvePðkÞ can be analysed with the load factor [25] which is the ratio ofmaximum to mean power:

LF ¼1N

PNk¼1PðkÞ

maxk

PðkÞ ð5Þ

The load factor varies between zero and one. A low value is anindicator of high power variations, as the maximum power is highcompared to the mean value. Conversely, a high value indicates asmooth demand and low variations.

When individual household loads are added they coincide moreor less depending on end-use composition and ultimately on activ-ity patterns. This effect must be reproduced by the stochastic mod-el. Coincident behaviour can be described by the coincidence factor[25]:

CF ¼maxk

PðkÞX

i

maxk

PiðkÞ,

ð6Þ

where the aggregate demand PðkÞ is the sum of the partial loadsPiðkÞ. The coincidence factor thus relates the maximum of theaggregate load to the sum of the maximum values of the partialloads. If the partial-load maxima all appear at the same time, thecoincidence factor equals one. If the maxima are spread out, thecoincidence factor assumes a lower value.

J. Widén, E. Wäckelgård / Applied Energy 87 (2010) 1880–1892 1887

4.2. Validation results

4.2.1. Aggregate demandModelled average load curves for the large set of detached

houses and apartments are shown, together with the correspond-ing ones in the EL-SEA-2007 data set, in Fig. 6. Since the TU dataset is the same as in Ref. [9] and since the activity-to-power con-version model also is based on this paper, the results are similarto those presented there.

There is an overall correspondence between measured andmodelled data. The diurnal distribution of end-use loads is, if notexactly reproduced, very close. In particular, differences betweenapartments and detached houses are captured, as well as differ-ences between weekdays and weekend days. The latter differencesinclude a higher weekend demand and a shifting of the demand to-wards mid-day on weekends. The main deviance between mea-sured and modelled data is the more variable modelled demand.This was also found in Ref. [9] and occurs because of fewer datapoints in the TU data on which the transition probabilities arebased than in the measured data. A larger TU data set would makethe distribution of transition probabilities and the aggregate curvesmoother.

(a) Detached houses, weekday

1 12 240

100

200

300

400

500

600

700

800

900

Hour

Wh/

h

1 12 240

100

200

300

400

500

600

700

800

900

Hour

Wh/

h

Model EL-SEA-2007

(c) Apartments, weekday

1 12 240

100

200

300

400

500

600

700

800

900

Hour

Wh/

h

1 12 240

100

200

300

400

500

600

700

800

900

Hour

Wh/

h

Model EL-SEA-2007

Cold appliances Lighting Cooking Dishwashing

Fig. 6. Annual averages of daily load curves obtained with the model and in the EL-SEA-2min basis during one summer and one winter week to estimate the annual load curve.

Annual total electricity demand estimated with Eq. (4) for thesimulated data and EL-SEA-2007 are shown in Fig. 7. The overallpattern is similar for measured and modelled data, with deviationsfor some end-uses. The total specified demand is somewhat under-estimated in detached houses and overestimated in apartments.The calculated additional categories compensate for thesedifferences.

To conclude, the applied parameter set gives a reasonablereproduction of aggregate demand, both in terms of daily distribu-tion and total demand.

4.2.2. Individual householdsFig. 8 shows an example of household electricity demand of one

modelled household and one measured household from TU/EL-SEA-2007 over 2 weeks of the whole measured and modelled 4-week period. The random patterns are similar, with recurring highpeaks and smaller demand variations and with variations betweenfast and slow changes in power. Naturally, since these are exam-ples of individual households, the exact peak and off-peak valuesdiffer between the curves.

Fig. 9 shows the total period demand for different householdsizes in modelled and measured data. The variability within the

(b) Detached houses, weekend day

1 12 240

100

200

300

400

500

600

700

800

900

Hour

Wh/

h

1 12 240

100

200

300

400

500

600

700

800

900

Hour

Wh/

h

Model EL-SEA-2007

(d) Apartments, weekend day

1 12 240

100

200

300

400

500

600

700

800

900

Hour

Wh/

h

1 12 240

300

600

300

400

500

600

700

800

900

Hour

Wh/

h

Model EL-SEA-2007

Washing/drying TV Computer Stereo Additional

007 data set. Two hundred detached houses and apartments were simulated on a 1-The parameter sets in Tables 7 and 8 were applied.

(a) Detached houses (b) Apartments

0

200

400

600

800

1000

1200

1400

Col

d ap

plia

nces

Ligh

ting

Coo

king

Dis

hwas

hing

Was

hing

/dry

ing

TV

Com

pute

r

Ster

eo

Addi

tiona

lEnd-use

kWh/year

ModelEL-SEA-2007

0

200

400

600

800

1000

1200

1400

Col

d ap

plia

nces

Ligh

ting

Coo

king

Dis

hwas

hing

Was

hing

/dry

ing

TV

Com

pute

r

Ster

eo

Addi

tiona

l

End-use

kWh/year

ModelEL-SEA-2007

Fig. 7. Total annual electricity demand for different end-uses obtained with the model and in EL-SEA-2007. Simulations as in Fig. 6. Annual demand was calculated with Eq.(4).

0 168 3360

2.5

5

Hour

kW

(b) TU/EL−SEA−2007

0 168 3360

2.5

5

Hour

kW

(a) Model

Fig. 8. Examples of demand for one modelled household and one measured household from the TU/EL-SEA-2007 data set during 2 weeks of the whole studied 4-week period.Simulations were run with 1-min time steps and resulting data averaged over 10-min intervals. Measurement data resolution is 10 min.

1888 J. Widén, E. Wäckelgård / Applied Energy 87 (2010) 1880–1892

set of households is captured fairly well, although the same param-eter set is used for all households except the parameters for light-ing. The variations in the measured data are larger, but themeasured data follow roughly the more linear trend in the mod-elled data. Differences between modelled households arise mainlyfrom household size, but also from different activity patterns in de-tached houses and apartments, different lighting parameter setsand different insolation periods corresponding to measured peri-ods. Apparently, an important part of the variability in the mea-surement data is captured.

The modelled data must also be realistic in terms of load-pat-tern shape. Descriptive statistics of the modelled and measureddata, divided on the individual end-uses, are shown in Table 9.All measures were calculated for each individual household. Inthe table, evaluations of these measures are shown as mean valuesover all households. The statistics are similar for most end-uses.The most apparent deviance is for cold appliances. An inspectionof the measured data for cold appliances showed that occasionalhigh power peaks, not part of the ordinary cyclic load, raised thestandard deviation and even more so the load factor. Most impor-

tantly, properties of the modelled total household electricity loaddata are close to those of the measured ones in statistical terms.

One important feature of the load data for individual house-holds is the spread of demand on high and low power levels.Fig. 10 shows the mean power duration curve for the 14 house-holds, together with the standard deviation between the house-holds’ different duration curves, showing variability betweenhouseholds in terms of distribution on high and low power de-mand. The model reproduces the mean duration curve, which sug-gests that on average the spread on high and low power levels isrealistic. Variability between households regarding this distribu-tion is also reproduced for high power demand levels. For lowerlevels, the standard deviation decreases compared to TU/EL-SEA-2007. This is an effect of using the same appliance set for all house-holds. In reality, standby powers and levels of inactive power de-mand differ between households.

This is more clearly seen in Fig. 11 where the standard deviationin the whole measured and modelled data sets is shown, calculatedover all time steps and all households. The deviation followsroughly the aggregate demand curve (cf. Fig. 6) with increasing

1 2 3 4 5 60

100

200

300

400

500

600

Household size

kWh

ModelTU/EL−SEA−2007

Fig. 9. Total 4-week demand for 14 modelled households and correspondingmeasured households in TU/EL-SEA-2007.

J. Widén, E. Wäckelgård / Applied Energy 87 (2010) 1880–1892 1889

variability over the mid-day and evening hours. The modelled andmeasured variability are highly similar, except for the first hoursafter midnight when there is minimum household activity andonly standby use. Since the lack of variability occurs duringnight-time and at low demand levels, it can be considered non-critical.

Table 9Average descriptive statistics for the end-use-specific power demand of 14 modelled hoevaluated over the whole simulated and measured 4-week period.

End-use Mean (W) Std (W) M

Mod Meas Mod Meas M

Cold appliances 82 79 40 58 1Lighting 94 72 119 96 4Cooking 59 34 261 157 15Dishwashing 9 22 97 137 16Washing/drying 12 18 98 113 15TV 36 33 35 32 1Computer 45 71 21 46 2Stereo 7 8 4 3

Total 343 337 360 349 34

(a) Model

0 168 336 504 6720

1

2

3

Hour

Pow

er (k

W)

MEAN

MEAN ± STD

Fig. 10. Duration curves for the 4-week power demand in 14 modelled households and(MEAN) over all households is shown together with the standard deviation (STD) betwe

4.2.3. Load coincidenceRandom coincidence of loads has a smoothing effect on the

aggregate demand curve. Fig. 12 shows aggregate modelled andmeasured demand over 2 weeks of the whole 4-week period forall 14 households. The smoothing effect is clearly seen when com-paring the curves to Fig. 8. In Fig. 12 the fluctuations and random-ness as well as the regularities caused by random coincidence aresimilar for modelled and measured data. A lack of reported night-time activities in the TU data that the activity-generating model isbased on causes the somewhat sudden decrease in demand at mid-night. Since peak loads are less pronounced in comparison to themean load for the aggregate demand, the load factor should in-crease successively when more and more loads are aggregated.This effect is shown for measured and modelled data in Fig. 13.

To obtain the curves in the figure, loads were aggregated suc-cessively in random order. This procedure was repeated for a largenumber of load permutations and the obtained curves were aver-aged to yield the mean curves shown in the figure. Once again,as was the case with the load factors for single households, thereare deviances in absolute values. This is most pronounced, as be-fore, for cold appliances. However, the change in load factor withincreasing demand aggregation is about the same for measuredand modelled data for all end-uses.

A further test of the reproduction of load coincidence is to eval-uate the coincidence factor for aggregate modelled and measureddemand. Relevant demand periods were chosen based on theaggregate demand fluctuations in Fig. 6. The demand is roughly di-vided into three periods in which the power demand assumes

useholds and corresponding measurements in TU/EL-SEA-2007. All measures were

aximum (W) Minimum (W) Load factor

od Meas Mod Meas Mod Meas

30 448 0 0 0.632 0.25780 545 0 5 0.205 0.11400 2647 0 1 0.040 0.01266 1333 0 0 0.004 0.01143 1438 0 0 0.006 0.00720 146 20 10 0.301 0.21819 219 40 29 0.219 0.20241 29 6 4 0.167 0.292

23 3814 66 55 0.102 0.088

(b) TU/EL-SEA-2007

0 168 336 504 6720

1

2

3

Hour

Pow

er (k

W)

MEAN

MEAN ± STD

corresponding measured households in TU/EL-SEA-2007. The mean duration curveen the households.

00:00 12:00 24:000

100

400

600

800

Time

STD

TU/EL−SEA−2007Model

Fig. 11. Daily variation in standard deviation (STD) in the power demand of 14modelled households and the corresponding measured households in TU/EL-SEA-2007. STD calculated over all households and all time intervals of the 4-weeksimulation and measurement periods.

1890 J. Widén, E. Wäckelgård / Applied Energy 87 (2010) 1880–1892

roughly the same values: 00:00–06:00, 06:00–17:00 and 17:00–24:00. The coincidence factor was evaluated in each time frameon each of the 28 days. Averages for each time frame were calcu-lated and are shown in Table 10. The modelled and measured val-ues are very similar and the difference between night-time anddaytime coincidence is captured.

To conclude, the overall statistical reproduction of coincidentbehaviour is accurate both in terms of load factor change and coin-cidence factor.

5. Concluding discussion

5.1. Possible refinements and extensions

Although the validation of the model shows that it works satis-factorily in all the investigated aspects, a number of differentrefinements, extensions and modifications can be imagined. A pos-sible model refinement is more detailed modelling of certain end-uses, for example cooking. A larger and possibly more detailed TUdata set could make it possible to define more detailed activity cat-egories. It is also possible to use more extensive data on appliance

0 160

10

20

Ho

kW

(a) M

0 160

10

20

Ho

kW

(b) TU/EL−

Fig. 12. Aggregate demand for all 14 modelled households and the corresponding measmeasurement periods. Simulations were run with 1-min time steps and resulting data a

ownership to increase diversity among households. Tuning theMarkov chains with TU data covering longer time periods couldavoid the somewhat problematic under-reporting of night-timeactivities that results from TU diaries being written from the morn-ing onwards although they are supposed to cover all 24 h. With lar-ger TU data sets it would also be possible to divide householdcategories on more Markov-chain matrices to capture specificactivity patterns or coordinated habits (cf. Ref. [12]). However, asshown for the lighting model [10], this refinement is not expectedto have any substantial impact on the modelled data. To overcomediscrepancies between modelled and measured data, parameterssuch as the activity-to-power conversion schemes could be fine-tuned. For example, to make peak powers of the aggregate loadcurves match known peak powers, the activity-to-power conver-sion schemes could be varied to increase the fit.

It is also possible to adjust the model to more specific case stud-ies. If the model is applied to more well-defined sets of buildings,the activity-to-power profiles could be adjusted to match thoseof a known sets of appliances and the daylight availability in thelighting part of the model could be modified to match certain win-dow setups, obstructions and shading and insolation conditions.The transition probabilities in the Markov-chain model could alsobe adjusted, either by tuning them to another set of TU data, ifavailable, or by assuming values that are reasonable for a certainend-user category.

As mentioned in the introduction, the model could also be ex-tended to cover other end-use loads, such as hot water, space heat-ing and cooling demand, or thermal loads such as appliance excessheat and body heat. The activity model could easily be extended toa room-specific occupancy model for homes by making assump-tions on where certain activities are performed within a building.In building simulations where multiple loads are taken into ac-count, the advantage of the model is that all end-uses are corre-lated, as they are based on the same underlying activity patterns.Including insolation data, as is done in the lighting part of the mod-el, also preserves important correlations between energy use andinsolation, which is important when modelling utilisation of solarapplications, such as photovoltaics, solar heating and passivehouses.

It is important to note that although possible adjustments andimprovements of the model can be identified, such extensionsmust always be valued against increased complexity and relativeimprovement of model accuracy. Since computations are poten-tially time-consuming, especially if large numbers of householdsand time steps are involved, there should be a sound balance be-

8 336ur

odel

8 336ur

SEA−2007

ured households in TU/EL-SEA-2007 during 2 weeks of the 4-week simulation andveraged over 10-min intervals. Measurement data resolution is 10 min.

1 140

0.5

1

Number of households

LF

Cold appliances

1 140

0.5

1

Number of households

LF

Lighting

1 140

0.5

1

Number of households

LF

Cooking

1 140

0.5

1

Number of households

LF

Dishwashing

1 140

0.5

1

Number of households

LF

Washing/drying

1 140

0.5

1

Number of households

LF

TV

1 140

0.5

1

Number of households

LF

Computer

1 140

0.5

1

Number of households

LF

Stereo

ModelTU/EL−SEA−2007

Fig. 13. Change in load factor (LF) with increasing aggregation of demand. Comparison between 14 modelled households and the corresponding measured households in TU/EL-SEA-2007. Averages of curves obtained through successive aggregation of different permutations of household loads.

Table 10Coincidence factors for the aggregate demand of the 14 modelled households andcorresponding measurements in TU/EL-SEA-2007. Each time-frame value is anaverage over the 28 days in the measurement and simulation period.

Time frame Model TU/EL-SEA-2007

00:00–06:00 0.82 0.7306:00–17:00 0.43 0.4817:00–24:00 0.49 0.50

J. Widén, E. Wäckelgård / Applied Energy 87 (2010) 1880–1892 1891

tween complexity and output quality. This model has shown thathighly realistic demand patterns can be generated with relativelyfew assumptions and a simplified and transparent model structure.

5.2. Examples of applications

As mentioned in the introduction, the model is applicable in anumber of areas where a realistic user behaviour has to be takeninto account. Some of these are:

5.2.1. Small-scale distributed power generationThis is the research problem for which the model was specifi-

cally developed, but it is also an application that should be of inter-est for utility or grid companies in planning of distributedgeneration. When very small but widespread photovoltaic systemsare integrated in low-voltage distribution grids, overproduction ofpower that is unmatched to the local demand will lead to a voltagerise that may exceed prescribed limits. On the other hand, localpower generation that matches the demand will increase on-siteutilisation, counteract voltage drops along distribution feedersand decrease distribution losses. It is clear that a domestic electric-ity demand model like the one proposed in this paper, that in-cludes all features of real demand and maintains the negativecorrelation between lighting demand and insolation, would con-tribute greatly to make power-flow simulations of distributiongrids in residential areas more realistic. Simulations for a numberof Swedish low-voltage grids will be presented in a separate com-ing paper.

5.2.2. Building simulationsIf extended to a number of additional end-use loads, the model

would be a viable tool for building simulations. For indoor climate

simulations of low-energy or passive houses that were mentionedin the introduction, thermal loads such as body heat from thehousehold members and excess heat from electrical appliancesare easily included in the model by using appropriate activity-to-power conversion schemes. Here, the ability of the model to pre-serve correlations between different end-uses, modelled from thesame activities, is important. The influence of detailed, typicalhousehold activity patterns on the indoor climate of a Swedish pas-sive house has been measured in an experimental setup by Karre-sand et al. [29], based on the same TU data that are used in thispaper. A clear impact of both occupancy and use of electric appli-ances on daily indoor temperature fluctuations was observed. Ex-tended to include thermal loads, our proposed model wouldpermit similar building simulation studies to be performed, thatcould cover a wide range of building types, geographical settingsand time periods with a high degree of detail. Further research willinclude this extension and application of the model.

5.2.3. Demand side managementAlthough no such application of the model has yet been per-

formed, it could provide a basis for studies of demand side man-agement and energy efficiency. As the model structure separatesactivities from electrical appliances, the load profiles of differentappliances can be varied to see the effect on total electricity useand daily fluctuations of the load profile. Conversely, the behav-ioural part can be altered by varying the Markov-chain transitionprobabilities. In a similar way, the model could also be applied tosimulations of demand-response schemes. Active demand re-sponse, where household members change their electricity use inresponse, e.g. to price signals, could be modelled by dynamicallydecreasing or increasing the transition probabilities for certainactivities. Automatic demand response, which involves an auto-matic modification of certain appliance load profiles, could beintroduced by dynamically altering the activity-to-power conver-sion schemes, while the activity pattern generation remainsunchanged.

6. Conclusions

The validation of the proposed model structure has shown thatthe Markov-chain model produces activity patterns that realisti-

1892 J. Widén, E. Wäckelgård / Applied Energy 87 (2010) 1880–1892

cally reproduce a spread of different end-use loads over time. Witha relatively simple conversion model from activities to power de-mand, realistic demand patterns can be generated from theseactivity sequences. All important features observed in measureddemand are reproduced, including end-use composition, diurnaland annual variations in aggregate curves for total demand andindividual end-uses, demand variation over different time scalesin individual households, diversity among households and demandcoincidence resulting in successive smoothing of aggregate de-mand with increasing numbers of households. A number of appli-cations of the model are identified, some of which will beinvestigated further in future research and coming papers.

Acknowledgements

The work has been carried out under the auspices of The EnergySystems Programme, which is primarily financed by the SwedishEnergy Agency. Part of the work with the development of the activ-ity-to-lighting conversion model was carried out in a project fi-nanced by Göteborg Energi. Kajsa Ellegård and Kristina Karlsson,Department of Technology and Social Change, Linköping Univer-sity, are gratefully acknowledged for providing time-use data forestimation of model parameters and validation. The authors arealso grateful to Peter Bennich at the Swedish Energy Agency forproviding measurement data on household electricity used forcomparison with the model output.

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