models for generating place and time dependent urban energy demand profiles

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Models for generating place and time dependent urban energy demand

profiles

Jani Mikkola⇑, Peter D. Lund

Aalto University, School of Science, P.O. Box 14100, FI-00076 Aalto (Espoo), Finland

h i g h l i g h t s

A model for generating spatiotemporal electricity load profiles has been developed. The model can be used for different urban areas, also with little input data.

Spatiotemporal profiles are useful for studying smart grids and renewables in cities.

a r t i c l e i n f o

Article history:

Received 21 November 2013

Received in revised form 19 March 2014

Accepted 20 May 2014

Keywords:

Urban energy

Energy demand profile

Spatiotemporal power demandSustainable energy

a b s t r a c t

In this paper, we present a new model for generating spatiotemporal power demand data for urban areas

of the form P ( x, y, t ). The model is flexible and can be adjusted to different cases and local conditions. The

dimensions of the model are not restricted, but a typical case would comprise an hour-by-hour simula-

tion over a whole year with a spatial resolution from a few hundred meters up to several kilometers,

depending on the area to be covered. These kinds of load profiles are useful when analyzing, e.g., smart

grids, demand side management, and renewable energy in the urban context. The model was applied to

two cities, Helsinki with detailed input data available, and Shanghai with access to rough data only. In

both cases, the generated load patterns appeared logical in terms of empirical observations on how power

demand behaves in space and time.

2014 Elsevier Ltd. All rights reserved.

1. Introduction

Urban areas constitute more than half of all energy use today.

By 2040, about 65% of all people will live in cities [1] stressing

the importance of urban areas when seeking solutions for the

global energy-climate issues which will require reducing the car-

bon emission by more than half by the middle of this century

[2]. Simultaneously, the progress in distributed energy generation

relevant to urban areas has been impressive during the past few

decades. For example, wind power, bioenergy, and particularly

photovoltaic systems are approaching such a scale of use that

starts to impact on global scale [3,4]. Coupling local energy

production with local energy use is an attractive option for sustain-

able energy in the future. It has several benefits such as avoiding

large energy infrastructures and involving end-users in energy

investments.

Distributed generation in urban energy systems raises new type

of issues less typical for the present systems. For example, employ-

ing variable renewable electricity (RE) in large amounts requires

more flexibility from the energy system to match the temporal

and spatial differences between supply and demand. Solving these

issues is especially important for electric systems, which as such

have little inherent inertia, and RE seldom provides any major

energy storage capacity, contrary to fuel-based traditional energy

production.

When matching large-scale distributed renewable energy with

the urban energy demand, understanding the spatiotemporal

energy profiles will be important. The same kind of data is also

needed in optimizing the power system, and to be able to identify

the systemic innovations and improvements that enable reliable

and effective operation of the power system. On the supply side,

the spatial variations in local RE supply such as solar or wind

power may not become relevant until at large geographical dis-

tances, but on the demand side, the power load may vary strongly

from building to building, i.e., on a short spatial scale. The power

demand is affected by a large range of factors, such as type of con-

sumer, human behavior, cultural factors, time of year and weather.

http://dx.doi.org/10.1016/j.apenergy.2014.05.039

0306-2619/ 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +358 504332255.

E-mail addresses: [email protected] (J. Mikkola), [email protected]

(P.D. Lund).

Applied Energy 130 (2014) 256–264

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There are numeroustools and methods available to simulatedis-

tributed or sustainable energy system [5], but in most of these, the

urban demand profiles need to be estimated separately. Many of

the demand models are based on bottom-up approaches, where

the load profiles are generated by summing up single loads to pro-duce a temporal load profile for a city. Such models are found for

household electricity loads[6,7] and hot water profiles [7,8], includ-

ing alsohigh-resolution1-min datasets [9], and differentappliances

[10]. Heating and cooling demand of buildings can be modeled,

e.g., with thermal resistance–capacitance networks [7,11–13].

These methods seldom split the load spatially, but treat the load

as a single unit, e.g., a single household, building or a whole city.

Measured spatiotemporal data of power demand P ( x, y, t ) is sel-

dom available for larger areas, and thus, it typically needs to be

estimated. In the future, if smart metering will be extensively

deployed, such data may become more readily available. Measured

temporal hour-by-hour data P (t ) may be available through utilities

for a whole city, but without the spatial dimensions. Load profiles

as such are very essential to plan optimally sustainable urbanenergy schemes, to operate the power system effectively, or for

the electricity markets to function. Thus lacking spatial data could

be perceived a handicap for planning or operation of future distrib-

uted urban energy schemes. The aim of this paper is to fill this gap

by bringing forward an effective model for generating space and

time dependent energy demand data.

In practice, modeling the spatial energy demand component

P ( x, y) is more challenging than the temporal component P (t ). Pre-

viously, ZIP codes have been used to estimate the annual spatial

energy consumption in a city (NY, USA) [14]. Post codes have also

been used to describe spatial loads [15], but rather to identify

energy efficiency measures than to create load profiles. Spatial dif-

ferences have been studied on a national level [16,17], but typically

the spatial resolution is then coarse and the temporal dimension ismissing. Despite the lack of detailed spatial data in energy, many

other disciplines offer ample urban data in spatial form, which

could potentially be applied to energy as well. These include land

use studies, population and building densities [18–22], and city

growth patterns and topologies [23–26]. Models of urban land

use changes and growth could be linked to spatial load forecasting

to enable, e.g., the planning of future electricity infrastructure, such

as grids [27–29].

Geographical Information Systems (GIS) could be useful to pro-

vide spatial demand data of buildings having an indirect link to

energy demand, but mostly GIS has been found useful in assessing

the renewable energy resource potential, e.g., biomass resources,

wind speed, and solar radiation [30–33]. GIS has also been used

to depict the energy use of a building stock in a city [34] and topropose optimal locations for urban energy supply systems [35].

In the present paper, we describe a new approach to generate

spatiotemporal load profiles for cities on an hourly scale outgoing

from limited input data available. Basically we split the temporal

data P (t ) spatially to P ( x, y, t ) with adequate resolution to make

such data useful. Compared to past models for urban areas mainlybased on temporal profiles, we introduce here a clear improve-

ment. Through connecting the spatial and temporal dimensions

enables to consider the energy system as a whole, which is of

outmost importance, e.g., when introducing large-scale renewable

energy schemes in cities or planning smart grid solutions. To our

best knowledge, it is the first time that this type of a model for

generating spatiotemporal load profiles has been reported.

2. Model description

2.1. General

In the present method, the urban power demand or load profile

is composed of three major consumer classes: households, services

and industry. Similar type of class division has also been used in

other studies [16], as well as by utilities and statisticians [36–

38]. Each class can be further divided into more specific sub-clas-

ses. For example, the households’ category may include sub-classes

such as apartment houses, row houses, and single family houses.

The service sector may consist of offices, educational buildings,

healthcare, restaurants and commercial buildings.

Urban structures andland useare themost importantfactors that

define the spatial electricity load. Therefore, spatial data will be

required for each consumer class and sub-class over the whole city.

The data could take the form of, e.g., population or employee densi-

ties, floor areas of different building types, etc. (see Section 2.2).

Sometimes spatial statistics do not exist or they are too incom-

plete to be used in a city-scale. For these cases, we suggest to applywell-known spatial models from land-use studies to create spatial

densities for the consumer classes. Several functional forms are

available [18,20–23] and we use here an exponential density

model [39] of the form

Dðr Þ ¼ D0eaðr r 0Þ2 þ K ð1Þ

where r is the distance from the city center, r 0 is the distance at

which the density reaches its maximum value D0, and a > 0 is a

width parameter of the distribution. We have added a constant K

to Eq. (1) to describe situations where the density is strongly

peaked but it spans over the whole city. In a strongly-peaked case,

an exponential function without the term K would decrease quickly

to zero, and thus it would not describe correctly the consumer den-sities far away from the peak location r 0.

Nomenclature

Symbols A total floor area (m2)a spatial floor area density (m2/km2)D density of consumer class (/km2) f temporal distribution of load (–)

I energy intensity (MW h/m2/year)K density constant (/km2)P load profile (MW)Q total annual consumption (MW h/year)r distance from the city center (km)s scaling factor (–)t time step (h)

x, y spatial coordinates (km)a width parameter (1/km2)

AbbreviationsPV photovoltaicsRE renewable energy, renewable electricity

Subscripts0 location of the maximum densitycity city in totali, j consumer classk, l consumer sub-class

J. Mikkola, P.D. Lund / Applied Energy 130 (2014) 256–264 257

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In addition to the spatial data, the method requires annual

energy consumption data (MW h/year) of each consumer class. If

such data is unavailable, energy intensities (MW h/m2/year) of dif-

ferent building types and their floor areas could be used (energy

use = energy intensity floor area). To incorporate a temporal

dimension into the model, temporal load distributions or so called

base profiles are required. These are relative hourly load profiles of

the consumer classes or sub-classes over 1 year, their yearly inte-gral being scaled to 1.

2.2. Transforming temporal load data into a spatiotemporal form

Fig. 1 illustrates the basic principle and steps of our model. For

clarity, only the main consumer classes are shown leaving out the

sub-class division. In the following, the procedure for generating

the spatiotemporal load profile is described step by step.

Step 1: Splitting the total load P (t ) into consumer classes

Employing a bottom-up approach, the load profile can be calcu-

lated from the consumption of a single consumer and the number

of consumers. The temporal load profile P i(t ) of consumer class i

(service/households/industry) is given by

P iðt Þ ¼ Q i f iðt Þ; i 2 fservice;households; industryg ð2Þ

where Q i is the total annual consumption (MW h/year) of the con-

sumer class i and f i(t ) is the corresponding temporal base profile

(P

t f iðt Þ ¼ 1Þ. The total load profile of the city is then simply

P ðt Þ ¼X3

i

P iðt Þ ð3Þ

If a real total load profile is known, then Eq. (2) need to be

scaled to match with that by incorporating a scaling factor s, which

is calculated for each time step

sðt Þ ¼ P cityðt ÞP jQ j f jðt Þ

8t ð4Þ

where P city(t ) is the real total load profile. To match with the real

total consumption, Eq. (2) can then be re-written in the following

form:

P iðt Þ ¼ sðt Þ Q i f iðt Þ ð5Þ

Step 2: Detailed division of P i(t ) into sub-classes P ik(t )

Assume that the spatial distributions ( x, y) of the consumer clas-

ses and sub-classes are based on building floor areas (alternatively

spatial population/employee densities could be used). The con-

sumer class profiles P i(t ) in Eq. (2) can then be split into more spe-

cific sub-classes k, whose building floor areas are known. Similarly

to Step 1 and Eq. (5) above, we have

P ikðt Þ ¼ P iðt ÞP

l AlI l f lðt Þ AkI k f kðt Þ ð6Þ

where I k is the energy intensity of sub-class k (MW h/year/m2), f k(t )

is the base profile, and Ak is the total floor area of sub-class k,

defined as

Ak ¼

Z x

Z y

akð x; yÞ d y d x ð7Þ

where ak( x, y) is the spatial distribution of the floor area of sub-class

k (m2/km2). The fraction part in Eq. (6) is a scaling factor to ensure

that the total load profile (summed over i and k) matches with theP city(t ).

Step 3: Spatiotemporal sub-class load distributions P ik( x, y, t )

Next, the sub-class temporal load profiles P ik(t ) are transformed

into a spatiotemporal form with the help of the floor area densities

ak( x, y). The load profile in location ( x, y) can be written as

P ikð x; y; t Þ ¼ akð x; yÞ

Ak

P ikðt Þ ð8Þ

Step 4: Spatiotemporal total load profiles

Finally, the total consumption profile in location ( x, y) at time t

is obtained from Eq. (8) by summing overall consumer classes i and

sub-classes k:

P ð x; y; t Þ ¼X

i

Xk

P ikð x; y; t Þ ð9Þ

3. Application of the model to a case with known spatial

building data (Helsinki)

In the next two sections, the model for generating spatiotempo-

ral load data is applied to two cases: (1) Helsinki (Finland) where

spatial input data (buildings) is available, (2) Shanghai (China)

where spatial data is unknown. These two cases are quite

representative to real world cases. Table 1 summarizes key urbandata for these sites.

3.1. Input data for the Helsinki case

Helsinki is a medium-sized city in northern Europe consisting of

136 neighborhoods. Statistics Finland and City of Helsinki have col-

lected building and population data of the neighborhoods from

2011 [40,41], which is used here as the spatial input data. The

hourly power demand of the city [42] is shown in Fig. 2, and it will

be allocated to each neighborhood based on the building stock of

that area. The building input data consists of 13 different building

categories, which are divided into three consumer classes i: house-

holds, services, and industry (see Table 2).

The base profiles used for different consumer classes weretaken from [37] (so-called standard load, based on German experi-

ences). This data set includes an own profile for households (code

H0), which was used for all building types in the consumer class

‘‘Households’’. The profiles used with service and industrial sectors

are presented in Table 3. These profiles cover the whole year

(8760 h) and were used as the base profiles f i(t ) and f k(t ) in Eqs.

(5) and (6). Average hourly base profiles for the three consumer

classes are presented in Fig. 3. The peak load of the service and

industry sectors is at noon, while the household profiles peak in

the evening and in the weekend, as expected.

In addition to the base profiles, the total annual consumption in

each consumer class is needed. In 2011, Helsinki had a residential

electricity consumption of 1,297 GW h, an industrial consumption

of 285 GW h and a service sector consumption of 2,876 GW h [36].Energy intensities of building types are needed for Eq. (6), and they

are presented in the second column of Table 4.

Fig. 4 shows how the building stock is distributed within the

city (here only the whole building stock and residential buildings

are shown). The structure is quite typical to any capital city: the

office buildings are mainly located in the city center whereas the

residential buildings are distributed more evenly throughout the

whole urban area.

Table 4 summarizes the building stock distribution: almost 60%

of the total floor area comes from the residential buildings, 30% are

service buildings and 10% industrial and storage buildings. The last

column gives the spread (min–max) of the building types found in

the neighborhoods. The borders of the districts in Helsinki have

been designed to form as unified entities as possible, so that simi-lar type of functions and buildings form one district [45].

258 J. Mikkola, P.D. Lund / Applied Energy 130 (2014) 256–264



Fig. 1. Schematic illustration of the spatiotemporal load model.


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3.2. Results and validation

Based on the data in Section 3.1 and the method described in

Section 2, the profile P ( x, y, t ) was calculated for each hour of the

year, which gives a matrix of 136 ( x, y) 8760 (t ) values. The upper

limit of the number of nodes in the model depends on the com-

puter memory capacity.

Fig. 5 illustrates typical spatiotemporal load profiles obtained.

The power demand peaks in the city center at noon or in the early

afternoon, whereas in the outer suburbs of the city with high share

of residential buildings, the peak occurs around 7–8 pm (See also

Supplementary Information for an animation of dynamics of the

load).

The peak load in the neighborhoods over the whole year is

shown in Fig. 5(d). The highest values of the peak load are foundin the city center and in its immediate vicinity, e.g., a level of

80 MW/km2 is reached in the beginning of February, whereas in

typical residential neighborhoods some kilometers away from

the center, the peak load drops to about 3–6 MW/km 2.

Fig. 6 shows the relative temporal load profiles of three districts

(locations shown in Fig. 3) of Helsinki. Kluuvi is a downtown dis-

trict with a lot of commercial and office buildings, whereas the dis-

trict of Puistola is located north of the city center with detached

residential buildings mainly (90% of total building floor area).

The district of Punavuori is a mixture of both types, and though

it is next to the city center, the share of residential multi-storey

apartments is significant. During the peak hours, the power

demand in these districts is more than two times higher than that

of the off-peak night hours.The profiles in Fig. 6 reveal the different behavior of the three

districts: in the downtown (Kluuvi), the electricity consumption

peaks during the working hours, whereas in the residential area

(Puistola), the peaks occur in the morning and in the evening.

During the weekends, the differences in the demand between the

residential and office areas are significant. Residential areas reach

high demands on weekends too, whereas in the office areas, the

demand stays clearly below the weekdays.

Strict validation of the simulation of the spatiotemporal profiles

is difficult at this stage due to lack of measured data, but could be

feasible in the future when the planned Smart Metering scheme in

Helsinki is fully accomplished. Therefore, we settle here for a sim-

ple validation exercise in which the annual aggregated load values

are compared against the measured ones. For the residentialsector, the model gives an annual consumption of approximately

Table 1

Summary of urban information for the case studies [36,38,40,41].

Helsinki Shanghai

Population (millions) 0.60 23

City area (km2) 215 6340

Population density (1000/km2) 2.8 3.6

Maximum population density (1000/km2) 28 36

Electricity demand (TW h/year) 4.6 120

Peak electricity demand (GW) 0.81 23

Fig. 2. Load profile P (t ) of Helsinki city [42].

Table 2

Consumer classes and sub-classes in the Helsinki case.

Consumer classes Households Services Industry

Sub-classes Detached houses Commercial Industry

Row houses Office Storage

Apartment houses (<4 floors) Traffic

Healthcare

Apartment houses (P 4 floors) Recreational

Education

Table 3

Data sources for the base profiles.

Building

type

Load profile [37]

Commercial G4 Stores and hairdressers

Office G1 Business, working days 8–18

Traffic G1 Business, working days 8–18 + G3 Business,

continuous + G6 Business, weekends

Healthcare G3 Business, continuous

Recreational G2 Business with evening consumption

Education G1 Business, working days 8–18

Industry G1 Business, working days 8–18 + G3 Business, continuous

Storage G3 Business, continuous

Others G0 Business, general

0 20 40 60 80 100 120 140 1600

0.5

1

1.5

2

Hour S h a r e o f w e e k l y c o n s u m p t i o n ( % )

Households

ServiceIndustry

Fig. 3. Examples of base profiles f (t ) of the three consumer classes for Helsinki.

Table 4

Data about the energy intensity and distribution of the building types in Helsinki

[40,41,43,44].

Building type Energy intensity

(kW h/m2)

Share of total

floor area (%)

Range of shares

between districts (%)

Detached house 60 7.4 0–97

Row house 45 4.5 0–81

Apartment house

(<4 floors)

30 11.8 0–54

Apartment house

(P 4 floors)

30 35.6 0–96

Subtotal – 59.3 0–98

Commercial 93 4.1 0–57

Office 86 12.8 0–73

Traffic 90 3.6 0–50

Healthcare 96 2.9 0–69

Get-together 230 2.7 0–69

Education 74 4.2 0–58


Industry 73 7.3 0–80

Storage 37 2.5 0–60


Other – 0.7 0–33


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1,500 GW h (1,300); for the service sector 2,800 GW h (2,900), and

for the industrial sector 260 GW h (290), where the numbers in

brackets are the real ones. The numbers coincide within a 15% mar-

ginal which can be perceived satisfactory.

4. Application of the model to a case with unknown spatial

building data (Shanghai)

In the next case, Shanghai (China), detailed spatial input data

was not available, for which reason Eq. (1) was used to depictmathematically the spatial consumer class densities.

4.1. Input data for Shanghai

The yearly electricity consumption in Shanghai was 129.6 TW h

in 2010, of which 55% went to the industrial and 13% to the

residential sector [46]. The hourly load profile of the whole city

[42] is shown in Fig. 7; the power demand reaches its maximum

during the summer months mainly due to the air-conditioning

demand.

The city is officially divided into 16 districts and one county

(= island which is neglected here). Spatial distributions for Shang-

hai can be estimated through known population densities in these

0

2.5

5.1

7.6

10

13

15

18

20

1 0 0 0 0 0 m

2 / k m 2

Puistola

Punavuori Kluuvi0

2.5

5.1

7.6

10

13

15

18

20

1 0 0 0 0 0 m

2 / k m 2

All buildings Residential buildings

Fig. 4. Example of spatial distributions (floor area) of selected building types for the 136 neighborhoods of Helsinki. The location of 3 suburbs is shown to be used in Fig. 6.

0

7.5

15

23

30

38

45

53

60

M W / k m 2

0

7.5

15

23

30

38

45

53

60

M W / k m 2

0

7.5

15

23

30

38

45

53

60

M W / k m 2

0

10

20

30

40

50

60

70

80

M W / k m 2

(a)

(c)

(b)

(d)

Fig. 5. Example of the spatial load (MW/km2) in Helsinki during a typical working day (a–c) and during peak load conditions in early February (d). (a) 2–3 am, (b) 11–12 am,

(c) 7–8 pm, (d) Peak load.


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districts. Population is strongly concentrated in the city center. The

most populous district of the downtown Shanghai, Hongkou, had a

population density of over 36,000 per km2 in 2011 [38]. The outer-

most districts have densities of 1,000–2,000 /km2. The consumer

categorization used in this case is presented in Table 5; the

category ‘Others’ includes mainly service-type of activities.

As the spatial resolution of the data above was not adequate for

a detailed analysis, Eq. (1) was fitted (by the method of least

squares) into measured data from the 16 districts to describe the

urban structure more in detail. Fig. 8 demonstrates the resulting

spatial densities of three consumer categories: households (popu-

lation density), industrial (employee density) and office sector

(floor area/km2) (detailed parameter values are given in Supple-

mentary Information). For comparison (not shown), all buildingdata from Helsinki was organized in similar format than in Fig. 8.

This yielded quite a similar curve as the office sector in Shanghai

within 0–5 km from the city center, but in the interval 6–15 km,

the data spread was much larger probably due to a better spatial

resolution and a more heterogeneous building stock than in

Shanghai.

4.2. Results

Figs. 9 and 10 show examples of the spatiotemporal load gener-

ated with the model and the input data from above. The city center

is located at coordinate (0 km, 0 km) in Fig. 10 (spatial distribu-

tion), In the simulations, the city was divided into squares of

1 km 1 km, each attached with consumer class densities from

Fig. 8. The model presented in Section 2 was then applied to these1 km2 squares.

The temporal behavior of the modeled load (Fig. 9) in the city

center and outskirts resemble each other because all consumer

classes were assumed to be spread throughout the city as shown

in Fig. 8 and, e.g., specific industrial zones as in the Helsinki case

could not be distinguished. Another reason is the high share of

the industrial power consumption, and industries being spread

all over the city.

The dominance of the industrial sector may also be the reason

for not observing evening peaks from the household sector, which

was typical in the Helsinki case. The effect of households can be

seen in Fig. 9 when comparing the demand during the weekdays

and weekends. The relative difference between the weekend and

weekday demand diminishes when moving away from the citycenter.

0 20 40 60 80 100 120 140 1600.2

0.4

0.6

0.8

1

1.2

Hour S h a r e o f w e

e k l y c o n s u m p t i o n ( % )

KluuviPunavuori

Puistola

Fig. 6. Relative load profiles of three different types of districts in Helsinki. Kluuvi is

a district in the city center with a lot of office buildings, Punavuori has both offices

and multi-storey apartments, and in Puistola, the share of residential buildings

(mainly detached houses) is 90%.

0 1000 2000 3000 4000 5000 6000 7000 80000

5

10

15

20

Hour

E l e c t r i c l o a d ( G W )

Fig. 7. Hourly electricity demand in Shanghai [42].

Table 5

Consumer classes and sub-classes in Shanghai case, and the base profiles [37] used

with sub-classes of consumer class ‘‘Others’’.

Consumer

classes

Households Industry Others Base-load profiles:

Sub-

classes

Households Industry Commercial G4 Stores and

hairdressers

Education G1 Business, working

days 8 am–6 pm

Healthcare G3 Business,

continuous

Hotels G2 Business, evening

consumption

Offices G1 Business, working

days 8 am–6 pm

Storage G2 Business, evening

consumption

Others G0 Business, general

Fig. 8. Spatial density profiles of the three consumer classes in Shanghai.

0 20 40 60 80 100 120 140 1600

10

20

30

40

50

60

Hour

C o n s u m p t i o n

( M W h / k m

2 )

0 km

2 km

4 km8 km

15 km

30 km

Fig. 9. Simulated temporal load of Shanghai at different distances from the city

center.


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Fig. 10 shows that the simulated peak power consumption

exceeds 60 MW/km2 in the city center, which is somewhat lower

than in down-town Helsinki. This is explained by the coarser spa-

tial resolution of the background sources used for generating the

input data (the area of the densest district in Shanghai was

23 km2, vis-à-vis 0.33 km2 in Helsinki). If the source data in Shang-

hai had more detailed spatial resolution (e.g., 1 km2), the peak

power would most likely exceed 500 MW/km2 due to the high-rise

office buildings dominating the Shanghai business center. Now, the

effect of these buildings is spread over an area of 23 km2.

Fig. 10 demonstrates a strong decline in the power demand ver-

sus the distance from the city center. At a distance of 10 km from

the city center, the peak demand has dropped below 20 MW/km2, at 15 km below 5 MW/km2, respectively. The corresponding

average power demand is ca 10 MW/km2 and 3 MW/km2, respec-

tively. In the city center, the average demand is 30–40 MW/km2.

5. Conclusions

As measured spatiotemporal load data with sufficient resolu-

tion for urban areas is seldom available, generating data through

modeling is the primary option for detailed urban energy analyses.

Available models rarely consider simultaneously the spatial and

temporal dimensions in the demand profiles. In this paper, a new

model was presented for simulating the power demand in cities

both in space and time. The model enables creating detailed pro-

files with a good spatial and temporal resolution. The model isbased on readily available geographical statistics of cities.

Spatiotemporal load data of the form P ( x, y, t ) is most useful for

investigating a variety of energy options for urban areas, such as

distributed energy generation or optimizing local renewable elec-

tricity supply with the demand. The data enables detailed analyses

on the operation of an urban energy system, on a city scale or

locally within a certain district of the city. Spatiotemporal data will

help to develop energy schemes with high renewable electricity

shares. For example, the identification of demand patterns could

help in locating RE power, such as PV, more optimally closer to

the demand side and avoiding overloading the electric network.

The usefulness of this data is most obvious to the design of Smart

Grid or Demand-Side Management (DSM) measures.

The standard version of the model relies on both temporaland spatial data from the urban area which is aggregated and

convoluted into a spatiotemporal from. For cases with very limited

access to input data, an algorithm to generate spatial profiles was

included. The spatiotemporal model has several degrees of free-

dom: size of urban area, spatial and temporal intervals, number

of consumer sectors, etc. This enables to adjust the model to differ-

ent cases and local conditions.

The spatiotemporal model was applied to two cases, one

(Helsinki) with detailed input data available, and another

(Shanghai) with access to rough data only. In both cases, the load

patterns appeared logical in terms of empirical observations on

how power demand behaves in space and time. Naturally, gener-

ated load profiles are always synthetic information and can never

exactly match the momentary power demand in a certain point,but when aggregated to the whole city level, the macro-scale fit,

e.g., on a yearly scale, is good.

Acknowledgments

The financial support of the Fortum Foundation and Finnish

Academy (Project number 269795) in cooperation with the Conicyt

of Chile is greatly appreciated.

Appendix A. Supplementary material

Supplementary data associated with this article can be found,

in the online version, at http://dx.doi.org/10.1016/j.apenergy.

2014.05.039.

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