Pergamon
PII:
Solar Energy Vol. 70, No. 3, pp. 255–261, 2001
 2001 Elsevier Science Ltd
S 0 0 3 8 – 0 9 2 X ( 0 0 ) 0 0 0 9 8 – 0 All rights reserved. Printed in Great Britain
0038-092X / 01 / $ - see front matter
www.elsevier.com / locate / solener
SOLAR ENERGY AND GLOBAL HEAT BALANCE OF A CITY
CLAUDE-ALAIN ROULET†
´
´
ˆ
´ ´
Laboratoire d’Energie
Solaire et de Physique du Batiment,
Ecole
Polytechnique Federale,
Lausanne,
LESO-PB, EPFL, CH 1015 Lausanne, Switzerland
Abstract—The global energy balance of a city involves numerous energy flows and is rather complex. It
includes, among others, the absorbed solar radiation and the energy fuels on one hand, and the heat loss to the
environment — by radiation, convection and evaporation — on the other hand. This balance generally results
in a temperature in the town that is slightly higher than in the surrounding country. Using solar energy saves
imported fuels on one hand, but increases the absorption of solar radiation on the other hand. Simple, steady
state models are used to assess the change of heat released to the environment when replacing the use of
classical fuels by solar powered plants, on both the global and city scale. The conclusion is that, in most cases,
this will reduce the heat released to the environment. The exception is cooling, for which a good solar
alternative does not exist today.  2001 Elsevier Science Ltd. All rights reserved.
global warming 1 . The carbon dioxide resulting
from combustion is certainly of greater importance, but this is not the issue addressed in this
paper. The heat generated by the combustion or
nuclear process, Q h , is related to the useful
energy, Q u , by:
1. INTRODUCTION
A city receives energy from the sun and from
imported fuels such as gas, oil, electricity, etc.
This energy is, sooner or later, converted to heat,
and this heat is released to the environment by
convection, conduction, radiation, and evaporation. The average temperature in the city results
from the balance between solar gains, internally
generated heat, and lost heat. This temperature is
usually larger than in the surrounding country.
The generalised use of solar energy in the city
on one hand saves imported fuels, thus tending to
lower the internally generated heat. On the other
hand, it increases the average solar absorption
coefficient, leading to increased gains.
The question is then: does the generalised use
of solar energy (passive solar heating, solar
heating collectors and photovoltaic cells) increase
or decrease the temperature in the city?
Q u 5 hh Q h
where hh is the conversion efficiency of the
process. Sooner or later, all the energy resulting
from the combustion is released in the environment as heat.
When the same amount of useful energy is
provided by solar energy, the amount of solar
radiation required for that purpose, Q s is:
Q u 5 h s Q s 5 hs as A s I s
(2)
where hs is the conversion efficiency from solar
radiation to useful energy (–), as is the absorption
coefficient of the solar collecting device (–), A s is
the solar collecting area (m 2 ), Is is the global solar
energy radiation per unit solar collecting area
(J / m 2 ).
This solar radiation is also, sooner or later,
converted into heat and transferred to the environment. Photosynthesis which converts a part of the
energy into matter is an exception, as long as the
produced matter is not converted back into heat
by combustion or metabolism.
2. WHOLE EARTH LEVEL
It is not the intention here to reproduce or
review all the investigations on global warming.
Only the effect of replacing heat from fossil
energy sources by solar heat is considered here.
Combustion of coal or oil for energy purposes and
nuclear power plants not only generate pollutants,
but also generate heat that slightly contributes to
1
†
(1)
Tel.: 141-21-693-4557; fax: 141-21-693-2722; e-mail:
claude.roulet@epfl.ch
255
It should be noted that the global effect of anthropogenic
energy is very small, since the solar absorbed by the Earth
(0.331.9 10 17 W) is about 8000 times the energy used by
mankind.
256
C.-A. Roulet
The solar collecting area covers a piece of land
or built area, which without this covering would
have absorbed some solar energy, the absorption
coefficient being the complement of the albedo, b.
Then, the solar energy absorbed without solar
collectors is:
Q s,0 5 (1 2 b)A s Is
(3)
The additional heat released to the environment
by a solar plant providing the useful energy Q u is
then:
3. TOWN LEVEL
Qu
Q s 2 Q s,0 5 ] 2 (1 2 b)A s Is
hs
5 (as 2 1 1 b)A s Is ¯ bA s Is
(4)
The last approximation being valid for good
solar collectors or solar cells, which have an
absorption coefficient close to one. It is assumed
here that long wave radiative heat loss is released
to the atmosphere, which is opaque to black body
radiation at low temperature.
Combining Eqs. (1) and (4), the net heat
gained by the earth when converting a fossil
energy plant into a solar one 2 is:
DQ 5 (Q s 2 Q s,0 ) 2 Q h
1
5 (as 2 1 1 b) A s Is 2 ]Q u
hh
(5)
Hence, using Eq. (2):
F
F
G
as 2 1 1 b
1
DQ 5 ]]] 2 ] Q u
hs as
hh
G
b
1
¯ ] 2 ] Qu
hs hh
(6)
The global balance may be either positive or
negative, depending on the initial albedo and the
relative values of the efficiencies of both plants.
In most cases however, a solar power plant would
result in less heat load to the environment, since
the albedo is rather small [0.3 for earth average
(Gassmann, 1996)].
As an example, replacing an average UCPTE 3
electricity power plant [hh ¯0.28 (Suter et al.,
1996)] by photovoltaic cells (hs ¯0,15) will decrease the produced heat from 3.6Q u to 2Q u if the
albedo is assumed to be 0.3, that is the Earth
average. A solar water heater (hs ¯0.4) replacing
2
a gas boiler (hh ¯0.8) will decrease the heat load
to the environment from about 1.25Q u to 0.75Q u .
Further details on hot water boilers are given later
in this paper.
Solar devices may also be installed on a high
albedo building, such as a lime-finished Mediterranean roof, where b¯0.9. Then the balance is
less favourable to solar devices: the PV system
will increase the heat production by 2.4 Q u , and
the solar water heated by Q u .
Any type of energy plant is considered here, from water
heater to electricity plants.
3
UCPTE5Union for Coordination of Production and Transportation of Electricity.
Let us now consider the earth as a thermal
reservoir, and consider the energy balance between this reservoir and a town. There are several
differences if the boundaries of the considered
system is not the Earth but a town:
1. the heat can be directly transferred to the
surrounding country instead of radiated to the
space;
2. heat can be transferred not only by radiation,
but also by convection and evaporation, the
latter being very important;
3. the used energy is imported as a semi-finite
product. For example, the heat generated by
electric power plant is often released outside
the city, and only electricity is imported.
The urban climate depends on a complex
pattern of interactions (Wanner and Hertig, 1984).
Involved parameters are, among others, sky view
factor, surface roughness, water storage capacity
and evapo-transpiration, production of heat and
pollutant concentrations (Eriksen, 1980; Landsberg, 1981; Oke, 1982). We will however limit
ourselves to the built environment and address
only the difference in energy balance of buildings
using either classical energy resources, or
equipped with solar energy devices. Evapo-transpiration, a priori not modified by the use of solar
devices, will not be considered.
3.1. Space heating and passive solar heating
We address here the change in heat released to
the environment when existing, standard buildings
are replaced by new, passive solar buildings. The
seasonal average heat balance of a building can be
calculated according to EN 832 (1998) with an
acceptable accuracy. In a first and global approximation, the same model can be used for all the
buildings in a town. The energy used for heating
these buildings, Q h , is then:
1
Q h 5 [Q l 2 hu Q g ]]
hh
(7)
Solar energy and global heat balance of a city
where Q l is the heat loss of the buildings during
the considered time period, in joule, hu is the
utilisation factor of the gains, that is the part of
the heat gains that contribute to compensate the
heat loss, Q g is the heat (free) gains, including
internal gains, Q i , and solar gains Q s . of the
buildings, in joule hh is the global efficiency of the
heating systems.
The solar gains are expressed, as in Eq. (2)
Q s 5 as A s Is
(8)
The heat transferred to the environment by the
building, Q e , include not only the imported
energy, but also the free gains. Then:
1
Q e 5 Q h 1 Q g 5 ] [Q l 2 hu Q g ] 1 Q g
hh
(9)
In addition, the town is heated by solar radiation. The total heat gain of the city is then:
Q 5 Q e 1 (1 2 b)(A t 2 A s ) Is
(10)
where A t is the town area. Developing Eq. (10),
we get:
1 (1 2 b)(A t 2 A s )Is
(11)
where Q i represent the internal gains.
An immediate and obvious result is that the
heat transferred to the town can be reduced by
reducing the heat loss, Q l , using better thermal
insulation and heat recovery on exhaust air.
Increasing the heating system efficiency, hh , not
only reduces the heat load to the environment, but
also decreases the outdoor air pollution.
When existing, standard buildings are replaced
by new, passive solar buildings, the solar collecting area will be increased, say from A s0 to A s1 . At
the same time, the utilisation factor hu will
decrease because this factor decreases (but not in
the same proportion) when the gain increases (EN
832, 1998). The heat released to the environment
is changed by an amount equal to:
1
DQ 5 ][(2hu1 1 hu0 )Q i
hh
2 as Is (hu1 A s1 2 hu0 A s0 )]
1 [as 2 (1 2 b)] (A s1 2 A s0 )Is
hu0 A s0 . The global effect in most cases is a
reduction of the heat load to the environment.
As an example, let us change a typical residential building, having 0.07 m 2 effective passive
solar collecting area 4 per square meter floor area
and 5 W/ m 2 internal gains, to a passive solar
building with 0.2 m 2 / m 2 effective passive solar
collecting area. Applying Eq. (12) to this example
results in a decrease of released heat slightly
larger than 70 MJ / m 2 heated floor area. In this
example, we assumed that, for the heating season,
hh 5 0.8, hu1 5 0.7, hu0 5 0.95, Is 5 1400 MJ / m 2
(vertical, south facade), as 50.9, and b50.2.
3.2. Hot water
Active solar water heating is probably the most
popular use of solar energy. When used, solar
collectors often provide only a fraction, Fs , of the
hot water, the remaining energy being provided
by a classical plant (e. g. gas, oil, or electricity).
While producing a mass m of hot water, a
common water heater releases to the environment
a quantity of heat:
Q u mcDu
Q 0 5 ] 5 ]]
hh
hh
F G
Ql
hu
Q 5 ] 1 2 ] (Q i 1 as A s Is )
hh
hh
(12)
Since hu1 , hu0 , the effect of the internal gains on
the environment increases in passive solar buildings. In addition, the last term is also positive,
since A s1 . A s0 , and as ¯1. However, the second
term decreases the heat load, because hu1 A s1 .
257
(13)
where Q u is the useful energy calculated from the
mass, m, the heat capacity of water, c, and the
temperature difference Du between hot and cold
water. hh is the global efficiency of the hot water
plant. During the same time period, an area A s of
the roof is heated by the solar radiation and
releases some heat to the environment, namely
(12b)A s Is .
A solar water heater providing a fraction Fs of
the used hot water releases heat by two ways: the
solar radiation collected by the collector area —
that is as A s Is — ends sooner or later into heat,
and the classical boiler releases a fraction (1 2 Fs )
of the heat calculated by Eq. (13). Then, installing
A s square meter solar collectors on a roof for hot
water changes the energy balance of the town by:
Qu
DQ 5 [a 2 (1 2 b)]A s Is 2 ]Fs
hh
(14)
Since a ¯ 1 for solar collectors, a 2 (1 2 b) ¯ b.
For example, consider a person using 50 l hot
water at 508C per day. This corresponds to 3 GJ
per person and per year. In a European temperate
climate, where Is ¯4.5 GJ / m 2 for the whole year
4
This area is the area of a black hole absorbing the same
amount of solar energy than the real collecting area. It is
close to half the area of clear, non-shaded windows.
258
C.-A. Roulet
on a tilted collector, one square meter good solar
collector attached to a well designed hot water
generator can provide half of this energy (Fs 5
0.5). Assuming 70% efficiency for the classical
water boiler, DQ ¯ 2 0.8 GJ when b50.3. When
b50.48, DQ50 J. Therefore, the city gets more
heat when solar water heaters are installed on
white roofs.
The long wave radiative balance of the roof
does not change significantly, since hot water
collectors have a glass or plastic covering, the
emissivity of which being close to that of the tiles
or any other usual roof type.
3.3. Seasonal heating with solar collectors
Solar roofs now appear on the market: the tilted
or curved roof is entirely made out of solar flat
plate absorbers, without transparent covering,
which also ensure the water tightness (Rossy,
1995). For this purpose, the absorber and its
selective black coating should of course be weather resistant. This is a cheap and efficient way to
preheat warm water and to provide low temperature solar heating. Generalisation of this technique
will result in large solar collecting areas in urban
environment.
When such a system provides heat used ‘on
line’, that is with a storage time constant of about
a day, heat released to the environment can be
expressed by Eq. (10), and the effect of replacing
classical roofs by such solar roofs is modelled by
Eq. (12). This is valid during the heating season,
but during the rest of the year, the heat collected
in the absorber may not be used, and then:
DQ 5 [as 2 1 1 b)]A s Is
(15)
The city will then get more heat, since as . 1 2 b.
This is not recommended, especially in climates
requiring cooling. In addition, the long wave
radiative balance of the roof during the night is
worse with a solar roof coated with a low
emissive layer than with a standard roof, which
emissivity is close to 0.9.
Seasonal storage solves this problem. The
principle is to store the heat generated by the solar
collectors during the sunny season in a convenient
storage, usually dry ground or an unused ground
water reservoir (IEA, 1985). This has several
advantages:
1. solar radiation being much larger in summer
than in winter, the available heat for a given
collecting area will be larger, even when
taking account of storage losses;
2. collected heat is used in winter, and then does
not contribute to town overheating in summer;
3. solar collectors are cooled at a temperature
slightly higher than the storage temperature.
They can then be colder than common roofing
exposed to sun. This active insulation reduces
the cooling requirement of the building and
increases the summer comfort at the top level.
It also decreases the heat released to the
environment.
In this case, and on a yearly time period, the
change heat released to town by classical buildings is given by Eq. (6), the useful energy Q u
being in this case the heating energy use, Q h , of
the building. If an area A s of classical roofing is
replaced by solar roofing heating the long term
storage, the heat released is reduced by:
F
F
G
1
1
DQ 5 Q h ] 2 ]]sas 2 1 1 bd
hh ashs
1
b
¯ Qh ] 2 ]
hh hs
G
(16)
As an example, let us take hh 5 0.7; hs 5 0.4;
b 5 0.2 and as 5 0.95. Then DQ 5 1.03 Q h , that is
nearly the heat requirement of the building,
despite the large part of collected solar energy
that is lost at the storage boundaries.
3.4. Photovoltaic plants
It is generally recommended to integrate photovoltaic (PV) cells to roofs and facades of buildings. This reduces the impact on the environment
and the transportation loss of electricity. We have
seen that at a global level, the heat load is reduced
when replacing an average classical electric
power plant by PV cells. At the town level
however, the benefit is not the same, since the
heat from the electric power plant is released in
the country, while heat from integrated PV cells is
released downtown.
Heat gains of a city with standard, extra muros
plant providing the useful electric energy Q u is:
Q 0 5 Q u 1 (1 2 b)A t Is 1 other gains
(17)
If the power plant is replaced by intra muros
PV cells, the heat gain is — apart from the
unchanged other gains — the total collected solar
radiation:
Q 1 5 (1 2 b)(A t 2 A s ) Is 1 other gains
(18)
Note that as A s Is include photoelectric current
and heat released by the cells. The energy Q u is
Solar energy and global heat balance of a city
provided by the cells according to Eq. (2). The
town heat load change is then (Eqs. 18–17):
DQ 5 [as (1 2 hs ) 2 (1 2 b)]A s Is
¯ (b 2 hs )A s Is
(19)
The absorption coefficient, as , is close to one.
Therefore, the heat released to the town will
decrease as soon as the photovoltaic conversion
efficiency is larger than the average albedo of the
city. This is generally not the case with today’s
conversion efficiencies (10 to 20%). The balance
remains nevertheless favourable if intra muros
electric power plant is replaced by PV cells.
Roof area may not suffice, at today’s efficiency,
to completely replace electric power plants. For
example, a Swiss uses, on the average, 6600 kWh
per year. A 28 m 2 photovoltaic plant installed in
Lausanne produces 3000 kWh / year. Therefore, a
person in Lausanne needs about 60 m 2 PV cells to
cover its electricity requirement. This is approximately the building floor space occupied by that
person for living and working. So if the building
is more than one floor high, a PV roof will cover
only a part of the buildings need.
3.5. Cooling
The coefficient of performance, g, of a cooling
plant is the ratio of the useful pumped heat, Q u , to
the required final energy Q f . The heat released to
the environment is the sum of the pumped heat
and the required energy. Applying once more the
methods used above, the change in town heat load
when replacing classical cooling plants by solar
ones is:
(b 2 1)gc 1 asgc 2 asgs
bgc 2 gs
DQ 5 Q u ]]]]]]](Q u ]]]
asgsgc
gsgc
(20)
where subscript c is for the classical cooling plant
and s for the solar one.
The approximation is obtained by assuming
that as 51. It follows that replacing classical
cooling plants by solar ones decreases the heat
load to the city as soon as hs . bgc .
The coefficient of performance, gc , of classical
cooling plants with electricity powered compressors is between 2 (unitary conditioners) and 5
(large compressors, low temperature difference)
(ASHRAE, 1996, 1998).
Two solar systems may be considered:
1. PV cells with compressors, with a global
coefficient of performance between 0.3 and 0.6
when 15% efficiency is assumed for PV cells;
259
2. thermal solar collectors (30 to 50% efficiency,
depending on type and operating temperature)
with adsorption chillers with 0.7 , gc , 1.
gs may then vary between 0.2 and 0.6. The
replacement of unitary air conditioners by high
performance solar system (gs 50.5 or more) will
slightly lower the heat load in a low albedo town.
However, changing good air conditioning systems
(b ? gc ¯ 2) by today’s best solar systems will
increase the heat load in most towns.
Therefore, the best way to decrease the heat
load in towns resulting from cooling is to decrease the internal heat load, to develop the use of
efficient solar protections and to follow, as far as
possible passive cooling strategies (Van der Maas
and Roulet, 1991). Coupling the building with the
ground is also a good solution (Santamouris et al.,
1997).
4. DISCUSSION
In order to get some comparative figures, let us
roughly estimate the energy use per one average
person in an European temperate climate such as
Paris, Geneva or Lausanne, and the corresponding
reduction of the heat released to the environment
if solar systems replace classical ones. This
person occupies about 60 m 2 heated floor area,
including working place. These figures are presented in Table 1.
Active solar heating completes passive solar
heating, which can only cover a part of the heat
requirement. The savings resulting from these two
systems can then be added. Total reduction of
heat release can be reduced by 20 to 30 GJ per
person and year, representing 600 W average
power. This figure is small when compared to the
solar radiation received by the ground area occupied by that person. For example, a Parisian
lives on 50 m 2 ground area, and receives 200 GJ
solar radiation per year.
However, even if, in theory, the sun can cover
the entire energy demand of mankind, we should
not make the same mistake as our predecessors.
Mankind had successive monolithic policies,
Table 1. Energy use per person and approximate reduction of
released heat when replacing classical energy sources by solar
devices
Type of use
Amount used
(GJ / year)
Heat load reduction when
using solar device (GJ / year)
Space heating
20 to 30
Hot water
Electricity
Cooling
3
20 to 30
about 0
Passive solar: 10
Active solar: 10 to 20
1 to 2
About 0
No reduction
260
C.-A. Roulet
mainly based on one energy resource: slaves,
cattle, wood, coal, oil, or nuclear. In a sustainable
policy, we should aim to use only renewable
energy sources, but all possible ones, using every
such source where it applies at best.
The question raised at the beginning of this
paper: ‘‘does the temperature increase or decrease?’’ can nevertheless not be readily answered. Heat balance of a city is very complex,
and involves a pattern of interacting phenomena
that lead to urban climate, and hence to temperature (Hertig, 1995). Important phenomena are
solar radiation, long wave radiative balance,
evapo-transpiration and convection. Because of
the latter phenomenon, a local increase in released
energy may result in a slight decrease in temperature, the air being cooled by a convective plume
powered by the additional heat release. It is
generally acknowledged however that the temperature difference between downtown and surrounding country results mainly from differences
in evapo-transpiration.
It was nevertheless shown in this paper, by
simple calculations, that the amount of heat
released to the environment by human activities is
still a relatively small part of the heat balance of a
town, and that solar devices in most cases reduce,
and not increase, this heat release.
nevertheless be recommended even in this case,
since this reduces the combustion products emitted by classical energy resources, and these
products have a much larger influence on global
warming than absorbed solar heat.
NOMENCLATURE
As
At
b
c
Fs
Is
m
Qf
Qg
Qh
Qi
Ql
Qs
Qu
as
as
Du
hh
hs
5. CONCLUSIONS
Simple, steady state models were used to assess
the change of heat released to the environment
when replacing the use of classical fuels by solar
powered plants. Generalised use of solar energy
will in most cases decrease the heat load to the
environment, on the global scale as well as on the
town scale. This includes passive and active solar
heating, hot water solar heating, and cooling in
some cases. Active solar heating using solar roofs
and seasonal storage present the largest saving
potential where heating is needed.
Heat load from space cooling can best be
reduced by first reducing the internal heat load
and solar gains, by passive cooling measures, and
by using efficient conditioning systems.
The heat balance is close to zero for photovoltaic cells replacing classical power plant
erected outside the town, but it is favourable if the
replaced power plant were downtown.
It should however be pointed out that solar
devices installed on high albedo buildings, such as
lime-caulked buildings, globally increase the
amount of heat directly released by that building
to the environment. The use of solar energy can
hu
solar collecting area, m 2
town area, m 2
albedo for solar radiation
heat capacity, J /(kg K)
solar fraction, –
global solar energy radiation per unit solar collecting
area, J / m 2
mass, kg
final energy, J
heat (free) gains, including internal gains, Q i , and solar
gains Q s , J
heat generated by combustion or nuclear process, J
internal gains of the buildings during the considered
time period, J
heat loss of the buildings during the considered time
period, J
solar gains, J
useful energy, J
absorption coefficient of the solar collecting device, –
coefficient of performance of a cooling plant, –
temperature difference, K
conversion efficiency of a combustion or nuclear process, –
conversion efficiency from solar radiation to useful
energy, –
utilisation factor of heat gains in building, –
Acknowledgements—The author cheerfully thanks Jacques
Alain Hertig (LASEN, EPFL) for the careful proof reading of
the manuscript, the information on urban climate, and the good
advice he provided for the presentation of the balance.
REFERENCES
ASHRAE (1996). Systems and Equipment Handbook, ASHRAE, Atlanta.
ASHRAE (1998). Refrigeration Handbook, ASHRAE, Atlanta.
EN 832 (1998). Thermal Performance of Buildings — Calculation of Energy Use For Heating-residential Buildings,
CEN Standard, Brussels.
¨
Eriksen W. (1980) Klimamodifikation im Bereich von Stadten.
¨ . Joach. Jung. Ges. Hamburg 44, 161–165.
Veroff
`
´ ´
et Realites,
Gassmann F. (1996). Effet de Serre, Modeles
`
Georg, Geneve.
Hertig J. -A. (1995) Urban climates and air pollution in small
swiss cities. In Wind Climates in Cities, Cernak A. et al.
(Ed.), Kluwer Academic Publishers.
IEA (1985). Large scale thermal energy storage projects,
Document D 18, Swedish Council For Building Research,
Stockholm, (http: / / www.bsab.byggtjanst.se).
Landsberg H. -E. (1981). In The Urban Climate, p. 275,
Academic press.
Oke T. R. (1982) The energetic basis of the urban heat island.
Quart. J. Roy. Meteor. Soc. 188, 1–24.
Solar energy and global heat balance of a city
Rossy J. -P. (1995). In La Toiture Solaire d’Energie Solaire sa
´
in Concours de l’Energie
Renouvelable, Vol. No 26, Swiss
¨
Academy of Engineering Sciences, Zurich,
http: /
/ www.satw.ch.
Santamouris M., Mihalakou G. and Asimakopoulos D. N.
(1997) On the coupling of thermostatically controlled
buildings with ground and night ventilation passive dissipation techniques. Solar Energy 60, 191–197.
261
Suter P. and Frischknecht R. et al. (1996). In Oekoinventare
¨ Energiesysteme 3, Auflage, ETH Zurich.
¨
f ur
Van der Maas J. and Roulet C. -A. (1991) Night time
ventilation by stack effect. ASHRAE Trans. 97(Part I),
516–524.
Wanner H. and Hertig J. -A. (1984) Studies of urban climates
and air pollution in Switzerland. J. Clim. Appl. Meteor 23,
1614–1625.