solar energy and global heat balance of a city

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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

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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: [email protected] 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.

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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.

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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

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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.

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