UTILIZATION OF SOLAR ENERGY IN COLD CLIMATE Elena Tazeeva

UTILIZATION OF SOLAR ENERGY IN COLD CLIMATE  Elena Tazeeva
Elena Tazeeva
UTILIZATION OF SOLAR ENERGY
IN COLD CLIMATE
Bachelor’s thesis
Degree programme
March 2010
DESCRIPTION
Date of the bachelor's thesis
10. 03. 2010
Author(s )
Degree programme and option
Elena Tazeeva
Building Services Engineering Double
Degree Program
Name of the bachelor's thesis
Utilization of solar energy in cold climate.
Abstract
Solar radiation is a source of life on the Earth. The sun heats the atmosphere and the
surface of our planet. Because of the sun winds are blowing, circulation of water is
happened, seas and oceans are heated, and plants are growing. Nowadays people
know how to transfer solar radiation straightly into energy. The subject of the project
is to research the possibilities of utilization of solar energy in cold climate. At this
project the model of calculation solar energy is shown. Following factors are taken
into account: location, geographic latitude first of all; position of the Earth on the orbit
because of the rotation around the Sun; time of the day depend on Earth spinning
motion; solar energy absorption and solar radiation dispersion of clear atmosphere.
Next group of factors which influence on solar radiation are climatic factors. It
includes real weather conditions (clouds, rains, haziness), anthropogenic pollution
(impacts of different factories, traffic).
As an example of utilization of solar energy one family house in Tyumen (Russia,
Siberia) is taken. Now only natural gas is used for heating for this kind of buildings in
this region. Values of solar energy there are very low during winter period. That is
why it is decided to use solar energy only for heating hot domestic water during
summer period. Discount cash model is used for cost efficiency calculation. Project is
cost efficient. Investment cost of equipment which transforms solar energy into heat
looks too high in comparison with costs of natural gas or light oil. Sometimes it is not
cost-beneficial to use solar systems. However fossil fuel usage has a great influence
on the ecology of our planet.
Subject headings, (keywords)
Solar radiation, Solar heating, Collector, Cold climate, Solar energy, Heating system,
Direct solar radiation, Diffuse solar radiation, Angle of sight.
Pages
Language
63
English
URN
Remarks, notes on appendices
Tutor
Martti Veuro
Bachelor´s thesis assigned by
Content
Introduction ..................................................................................................................... 1
1.
General information about usage of energy ............................................................. 3
2.
Nature of solar radiation .......................................................................................... 5
2.1.
Influence of geographical and astronomic factors. ........................................... 5
2.2.
Influence of physical atmosphere properties .................................................. 12
2.3. Influence of climate factors. ............................................................................. 18
3.
Example of calculation. ......................................................................................... 19
4. Heating demand of one family house in Tyumen, Russia......................................... 28
4.1. Calculation of heating demand according to thermotechnical calculation. ........ 28
4.2. Calculation of heating demand according to the gas consumption. ................... 32
4.3. Total energy demand for heating and HDW ...................................................... 33
5. Usage of solar energy. ............................................................................................... 35
5.1. Solar house ......................................................................................................... 35
5.2. Types of solar collectors ..................................................................................... 37
5.3. Types of solar water heating systems ................................................................. 41
5.4. The operating principle of solar water heating system ....................................... 45
6. Summary ................................................................................................................... 47
Conclusion ..................................................................................................................... 51
Bibliography .................................................................................................................. 53
1
Introduction
Solar radiation is a source of life in the Earth. The sun heats an atmosphere and
surface of our planet. Because of sun winds are blowing, circulation of water is
happened, seas and oceans are heated, and plants are growing. Fossil fuels exist
because of sun. Nowadays people know how to transfer solar radiation straightly into
electricity and heat.
Solar energy became very popular. It has a lot of benefits. First of all solar
energy is free of charge. Of course it has an investment costs (costs of equipment) but
operating cost are very low.
The next point is that ecological situation in our world is so good, as we want.
So, we must try to prevent this situation and find solutions for ecological problems.
Fossil fuels such as coal, oil, and natural gas in one side are fundamental parts of
industry and the other side they are harmful for nature and environment. Using solar
energy we will have no impacts, it is absolutely environmentally friendly.
The next problem is so, that fossil fuels are not renewable. Of course we need
energy, and it´s consumption must be enough for normal life, but can we protect our
future? Solar energy is renewable, it is the greatest benefit.
Solar energy can be used for electric generation, for solar drying (solar croup
drying technology), for solar cooking, for distillation of water, and of course for
heating water. HVAC designers use solar energy in domestic hot water systems, in
heating systems (including floor heating), and in pool heating.
Solar thermal technologies are very common for southern countries. The reason
is that the total solar radiation is highest in the equator, especially in sunny, desert
areas. Amount of solar radiation depends on many factors. For example: geographical
location, cloud cover, hours of sunlight per day, etc.
The aim of my work is to answer the question: Is it possible to use solar
radiation in northern regions? The angle at which sun strikes the earth’s surface
2
changes during the year, so, the solar radiation changes. Thus, in northern countries in
winter, where the sun is low in the sky, solar energy is very low. So, it is a question,
can we use solar energy in this regions full year or only in summer time?
Because of cold climate maybe we can’t get high temperatures, so, I would like
to determine the potential ways of using these temperatures in systems.
I want to answer these questions using the example. My example is utilization
of solar energy in one family house in my native city Tyumen (Russia, Siberia). Now
only gas is used for this kind of buildings in this region. I would like to research is
there any possibility of using solar energy. Of course it is a question of cost also. I
would calculate costs efficiency of this project.
3
1. General information about usage of energy
Nowadays traditional ways of getting energy are used. Heat power plants and
hydroelectric power plants are built, nuclear power plants are popular in many
countries. These main branches of energetics are parts of global system, which is
named “blood-vascular system” of our civilization, provide living standard, but on the
other hand they damage environment.
It is known, that mineral resources are not renewable. But it is not the main
problem. The real problem today is their bad influence on nature. The main
imperfection of the fuel in thermal power plants is pollution of environment with
harmful emissions. Even modern power plants are not safe from ecological point of
view. In addition, production, treatment, and transportation have their harmful effect.
Hydroelectric power plants (produce 15% of total energy consumption) also
damage nature. Construction of dams on the rivers and large areas of storage ponds
can cause serious ecological problems.
Disadvantages of nuclear power stations are well known. Storage and treatment
of radioactive waste has very harmful effect. There is a risk of radiation pollution in
time of emergency, like in Chernobyl disaster.
Maybe thermonuclear power stations will be safe in future, many scientists are
involved in this project. Nowadays required total consumption of using energy is near
11,791 billion tones of equivalent fuel (one ton of equivalent fuel gives 11,63 MWh of
energy) /1/. This value rises all the time. Firstly because of increase in population (now
it is 6 billion people and it will be as predicted 7,4 billion by year 2020). Secondary
because of growth of people’s living standard, especially in developing and in highly
industrialized countries.
Global demand of energy will rise many times and will be 34 million tones of
equivalent fuel per year till 2020. This increasing of energy production will influence
4
too match on the Earth environment, and may become one of the reasons of global
warming.
Using of alternative or renewable energy sources can help to solve this
problem. They are more environmental friendly, than traditional source of energy.
Solar energy is the most attractive renewable resource. Solar energy comes to
the earth billions of years, and is involved to each process. It is totally ecologically
clean. Solar radiation must be used in a large scale to save the unique climate of our
earth.
Every year 1,03*1018 kWh of solar energy comes to the earth./1/ We can use
1,5% of solar radiation or 1,6*1014 kWh without an influence on Earth ecology
(without changes in climate and nature energy exchange). It is more than 100 times
higher, than total yearly energy consumption.
Solar radiation depends on time of the day, season, and weather conditions.
Average value of solar radiation on the Earth surface is not high. For example, when
angle of latitude is 40°, solar radiation is near 0,3kW/m2. /1/ It is five times lower, than
it is in the border of the atmosphere (1,4 kW/m2 ). Solar radiation must be collected
from large areas and accumulated.
Development of utilization of solar radiation becomes one of direction of public
policy in many leading countries. UNESCO, European Commission U.N.O., energy
department of U.S.A. are looking at this question. Worldwide organization of
development and spreading of energy technologies ODET is created and it works quit
well.
5
2. Nature of solar radiation
Solar radiation characteristics on the Earth surface.
Solar radiation is different in different places on the Earth. The reasons are:
1. Solar radiation is not perpendicular to Earth surface all the time.
2. Daylight hours are limited.
3. Part of solar radiation is absorbed and diffracted in clear atmosphere.
4. Solar radiation is absorbed and diffracted by clouds and anthropogenic
particles.
2.1.
Influence of geographical and astronomic factors.
Basic principle of calculation of total consumption of solar radiation in
different parts of the Earth are shown in figure 1.:
Figure 1. Scheme of inflow of solar radiation on horizontal surface./1/
6
Abbreviations on the Figure 1 mean:
S - area of horizontal surface;
ΘZ - angle of sight of solar radiation;
S*cos ΘZ - projection of area on the surface, which is perpendicular to
direction of solar radiation.
Flux of radiation or radiation power on the horizontal surface is ES┴ * S * cos
ΘZ , where ES┴ - density of perpendicular solar radiation per m2 (W/ m2). ES┴ is
maximum in January – 1410W/m2 and minimum in June -1315W/m2. Due to the
distance between the Sun and the Earth changes all the time. But for energetic
calculations constant average value can be used. ES┴ =1367 W/m2 , and it is named
solar constant. The same flux of radiation will be on the horizontal area S. Density of
radiation of this plane can be calculated:
E0hor= ES┴ * S * cos ΘZ / S = ES┴ * cos ΘZ
Formula 1 /1/
So, it is very necessary to estimate ΘZ – value, it changes every day of the year.
Angle of sight of solar radiation and the length of the day depends on following
factors:
1. Geographical coordinates of the surface, geographic latitude first of all;
2. Position of the Earth on the orbit because of the rotation around the Sun;
3. Time of the day depend on Earth spinning motion.
Geographic latitude
φM is an angle between the line, which connect point
(point M on the figure 2. is a site of interest) on the Earth plane with center of the
Earth and it’s projection on the equator plane.
7
Figure 2. Geographic latitude and angle of pitch of the Sun./1/
Position of Earth on the orbit is characterized by angle δn. It is an angle
between the line OC (Figure 2), which connect centers of the Earth and the Sun and
it’s projection on the equator plane. This angle is called angle of solar declination. We
should use it because it takes into account influence of inclination of the Earth axis.
The Earth axis is inclined on 66,50 for Earth orbit plane. (Figure 3)
Figure 3. Inclination of the Earth axis. /1/
8
Angle of solar declination changes all the time from +23,50 to -23,50 . +23,50 is on the
day of summer solstice, 22 of June. It is the longest day in the year, because Earth axes
is inclined by the northern end to the Sun side. -23,50 is on 22 of December . It is a day
of winter solstice, it is the shortest day in the year on the northern hemisphere.
Besides days of summer solstice and winter solstice there are days of autumnal and
spring equinox. They are 21 of Match and 23 of September. During this days the Earth
axes is perpendicular to the line, which connect center of the Earth and center of the
Sun. The angle of solar declination during this days is 0.
Position of the Earth on the orbit during the rotation around the Sun is characterized by
the angle of solar declination. It has a big influence on the around of solar radiation on
the horizontal plane on the given latitude. ΘZ - angle of sight of solar radiation is
minimum on the 22 of June and maximum on the 22 of December. ΘZ is average and
the same on 21 of Match and on 23 of September.
Angle of pitch of the Sun for every day can be calculated using the following formula:
δn=23,5 * sin ( 3600 * ( n-81) / 365),
Formula 2 /1/
where n is a serial number of the day in the year (reference point is the 1 of January)
Angle of solar declination value is positive in the period from spring equinox to
autumnal equinox and negative in other half of the year.
Angle of sight of solar radiation dependence on Earth spinning motion is characterized
by solar-hour angle ωs . It is measured on the equatorial plane between the projection
of the lines. First line connects point M with center of the Earth, second connect
centers of the Earth and Sun. ( it is shown on the figure 3. Geographic latitude and
angle of pitch of the Sun.)
Solar-hour angle ωS depends on the time of the day. In the middle of the day it is 0.
Every hour it is changed 150. Solar-hour angle can be calculated using formula:
ωs = k ωs * ( tsr – 12),
Formula 3 /1/
9
k ωs = 150/ hour. It is a coefficient of conversion of solar-hour angle into degrees;
tsr is a real daylight time in hours.
This formula implies that at the middle of the day tsr = 12h solar-hour angle will be 0,
ωs =0. Before the noon value of solar-hour angle is less than zero, ωs < 0. After the
noon value of solar-hour angle is more than zero, ωs > 0.
Solar time is differ from the time, which is used on this territory. For example in
Russia it is varies over legal time (1 hour for summer period and 2 hours for winter).
Mathematical expression for cosine of angle of sight of solar radiation on the
horizontal plane is:
cos ΘZ= cos δn * cos
φM * cos ωs + sin δn * sin φM
Formula 4 /1/
Time of the sunset and sunrise, length of the day, changes of the density of solar
radiation on horizontal plane (in the way without atmosphere or if it is transparent) can
be calculated according this formula.
Time of the sunset and sunrise, length of the day.
The angle of sight of solar radiation on the horizontal plane is 900 in the moment of
sunrise and sunset. It means that cos ΘZ= 0. Using this result in formula 4 can be
achieved:
cos ωs sunrise,sunset * cos δn * cos
φM = - sin δn
* sin
φM
Formula 5 /1/
Solar-hour angle for sunrise and sunset can be calculated according following formula:
ωs sunrise,sunset = arcos (- tg
φM * tg δn )
Formula 6 /1/
10
Before the noon value of solar-hour angle for sunrise is less than zero, ωs < 0. After the
noon value of solar-hour for sunset angle is more than zero, ωs > 0. So, absolute values
of time of sunrise and sunset are equal. They are opposite in sign:
tssunset = ωs sunset / k ωs+12
Formula 7 /1/
tssunrise = - ωCssunrise / k ωs +12
Formula 8 /1/
Value of the daylight hours is:
Ts = tssunset - tssunrise = 2 k ωs * arcos (- tg
φM * tg δn )
Formula 9 /1/
Using this dependents changes of density of radiation on horizontal plane during
daylight hours can be calculated (from sunrise to sunset).
Flux of solar radiation in the way of absolutely transparent atmosphere or without
atmosphere can be calculated:
W ohor 
t sunset
s
E o (t )  dt

hor
t sunrise
s
Formula 10 /1/
W ohor - flux of solar radiation.
Connection between local time and real solar time.
In previous calculations tsr - real daylight time in hours is used. Real daylight hours –
is a time which Sun is needed to go through the meridian where the site of interest is.
Value of daylight hours is not a constant. Sun cross the meridians in uncertain time
period. It happens because the visual moving of the Sun is determined not only by the
Earth spinning motion. It depends also on the rotation of the Earth around the Sun.
This motion is not uniform because the orbit of the Earth is elliptic. As a result, some
11
days of the year value of real daylight hours is more than average, and other days less
than average.
Difference between real daylight hours and average daylight hours on the meridian
can be determined by equation:
ttime = tsr - tsav ,
Formula 11 /1/
tsr = tsav + ttime .
Formula 12 /1/
t sav- average daylight hours;
ttime - time correction in minutes.
Approximate value of ttime - time correction can be found on diagrams or using
approximating function:
ttime = 229,2 * ( 0,000075 + 0,001868 * cos B - 0,032077 * sin B –
-0,014615 *cos 2B – 0,04089 * sin 2B.
Formula 13 /1/
Where B = 3600 * ( n - 1 ) / 365.
Nowadays zonal time is used. The whole Earth is separated into 24 time zone every
150 from Greenwich meridian. In every time zone time is fixed. This time depends on
the average position of the Sun in the highest point on middle meridian at 12 o’clock.
So, the average solar time and zone time are equal only on the middle meridian in
given time zone.
Difference between local average solar time and zone time can be estimated by
following formula:
tSMav = t zone + ( λM – λav ) / k ωs
t zone - zone time,
λM - longitude of the site of interest,
Formula 14 /1/
12
λav - longitude of middle meridian of concerned time zone.
Since on every meridian tsr = tsav + ttime , therefore:
tSr = t zone + ( λM – λav ) / k ωs + ttime .
Formula 15 /1/
Equation 14 shows relation between real solar time and local time in most of the
countries. But in Russia legal time is used. It means that 1 hour correction for the
winter time and 2 hour correction for summer time must be used. Equation 14 can be
modified for Russia:
tSr = tM - Δtleg + ( λM – λav ) / k ωs + ttime ,
Formula 16 /1/
where Δtleg - correction of legal time.
For calculation of local time on given meridian (when all corrections are taken into
account) following formula can be used:
tM = tSr + Δtleg + ( λM – λav ) / k ωs + ttime
Formula 17 /1/
According local time of sunset can be calculated:
tMsunset = 1 / k ωs * ( arcos(- tg
φM * tg δn ) + ( λM – λav ) ) + Δtleg - ttime +12.
Formula 18 /1/
2.2.
Influence of physical atmosphere properties
Solar energy absorption and solar radiation dispersion at clear atmosphere.
Direct solar radiation from cosmos is absorbed and dispersed by molecules of
atmospheric gases: nitrogen (N2), oxygen (O2), carbon dioxide (CO2), water vapor
(H2O), ozone (O3).
Absorption is happened when natural-vibration frequency of molecules and
radiation frequency of solar spectrum are the same. Radiation absorption in different
13
part of the solar spectrum by different gaseous vary. For example, N2 and O2 do not
reduce solar energy too much. They absorb radiation in ultraviolet spectrum, where is
small part of solar energy. Ozone influence is much higher. Ozone absorbs photons
with highest energy, these photons can be dangerous for nature. CO2 absorb infrared
spectrum in a small amount. Water vapor H2O can absorb more than
10% of
solar radiation.
Dispersion of solar radiation is due to molecules (molecular scattering) and
bigger particles like dust, smoke, micro drops of water (aerosol scattering). Because of
dispersion, photons don’t absorb. They change their direction. Some part of radiation
goes back to cosmos; another part comes down to the earth as diffuse radiation.
Decreasing of density and changes in spectrum of solar radiation at the expense
of absorption and dispersion depends on length of the trajectory of solar energy.
Scheme for calculation of this length is shown on figure 4:
Figure 4. Sunbeam’s trajectory in the atmosphere./1/
14
L
H
.
cos  Z
Formula 19 /1/
Thickness of the atmosphere is many times less than radius of the Earth, so we
can calculate it as plane-parallel layer. The Earth surface curvature when the Sun is not
higher than 10 degrees.
M-atmospheric mass is used to measure length of trajectory of sunbeam. When
sunbeams come vertically, M=1.
M 
1
.
cos  Z
Formula 20 /1/
Density of direct solar radiation on horizontal plane subject to it’s absorption
and dispersion in a clear atmosphere can be calculated:
Edirecthor= ES┴ *τ∑* cos ΘZ ,
Formula 21 /1/
Where τ∑ is a coefficient of direct light transmission. It depends on absorption and
dispersion of the atmosphere.
All types of absorption and dispersion of direct solar radiation are determined
by coefficients of transmission. Total coefficient of direct light transmission can be
calculated:
τ∑ = τabsorb * τdisp,
Formula 22 /1/
Where τdisp is a multiplication of coefficients of dispersion of solar radiation in the
atmosphere;
τabsorb is a multiplication of coefficients of absorption of solar radiation by ozone,
gaseous, water vapor ( τOз , τgas , τHгO ):
τabsorb = τOз * τgas * τHгO.
Formula 23 /1/
There are many methodic to determine density of solar radiation on horizontal
plane in a clear sky. Bird model is chosen in farther calculations. It includes simplest
15
equations of transmission coefficient. It takes into account absorption of solar radiation
by ozone, gaseous, water vapor, aerosol scattering, rayleigh scattering.
Correcting coefficient for horizontal plane for Russia was found by E.
Aronova:
For direct solar radiation:
Kdirect=1,14 – for winter period;
Kdirect=0,91 – for summer period;
For diffuse solar radiation:
Kdiffuse=1,05.
Subject to these coefficients density of direct solar radiation can be calculated:
Edirecthor= ES┴ *τR *τA *τOз * τgas * τHгO * cos ΘZ * Kdirect ,
Formula 24 /2/
Where τR coefficient of Rayleigh scattering is calculated by following formula:
τR =exp(-0,0903*(M*i)0,84,*( 1+ M*i + M*i1,01 )),
Formula 25 /2/
τA coefficient of aerosol scattering:
τA =exp(-τA´0,873 *( 1 + τA´ - τA´0,7088)* M*i)0,9108,
Formula 26 /2/
where τA´=1,832*α, if α=0,0314 – Angstrom coefficient of spectral turbidity.
τOз - coefficient of absorption of solar radiation by ozone:
τOз =1-0,1611*dOз * M*i*(1+139,48 * dOз * M*i )-0,3035-0,002715 *dOз * M*I *
*( 1+ 0,044 * dOз * M*i + 0,0003* ( dOз * M*i ) 2)-1 ,
Formula 27 /2/
where dOз – thickness of ozone layer at normal temperature and pressure. It is 0,32cm
for average latitude.
τgas - coefficient of absorption of solar radiation by gases:
τgas =exp(-0,0127 * M*i0,26).
τHгO - coefficient of absorption of solar radiation by water vapor:
Formula 28 /2/
16
τHгO = 1- 2,4959 * dHгO* M*i* (( 1+79,034* dHгO* M*i )0,6828 +
+6,385 * dHгO* M*i )-1 ,
Formula 29 /2/
where dHгO- water content (for winter period 1,3g/cm2 , for summer period 3,0g/cm2).
M*i- atmospheric mass corrected according position over sea level:
M*i= p*M i/1013,
Formula 30 /2/
where p= atmospheric pressure at site of interest.
Diffuse solar radiation
Sources of diffuse solar radiation on horizontal surface are:
1. Part of solar radiation, which is dispersed in the atmosphere.
2. Indirect reflection (direct and diffuse solar radiation, which comes back to the
atmosphere and is dispersed again).
Reflection qualities of the all surfaces can be characterized by value of albedo.
Albedo is a ratio between flux of reflected solar radiation and radiation which come
down to the surface. It is a coefficient of reflection. For example, albedo of the
ground is about 5-10%, albedo of snow is a maximum 30-90%. It also depends on
angle of the sunbeams.
Intensity of that part of solar radiation which is a result of indirect reflection
depends also on albedo of the atmosphere.
Density of the diffuse flux of solar radiation on the horizontal surface is
determined by:

Light angle;

Transparent of the atmosphere, haziness, cloudiness
17

Albedo of the Earth surface
Part of the diffuse solar radiation in a total flux of solar radiation increases
when M (atmospheric mass) increases too. It happens because losses of solar radiation
become less. When there is a haziness diffusing increase and density of diffuse solar
radiation increase. The same effect is when the albedo of the Earth surface increase.
Distribution of the diffuse solar radiation is not uniform. There are several
models of calculation of diffuse solar radiation. When the sky is not absolutely clear
even in fair weather conditions isotropic distribution model can be used. It means that
distribution of the diffuse solar radiation is uniform.
Value of the diffuse solar radiation is in proportion to that part of direct solar
radiation in atmosphere which does not come down to the Earth like direct solar
radiation. So, following formula can be used to calculate diffuse solar radiation:
Ediffusehor= ES┴ * cos ΘZ *τAA *τOз * τgas * τHгO *(0,5*(1-*τR)+
- Ba*(1- τAS))/(1- M*i + M*i 1,02 ) * Kd ,
Formula 31 /2/
where Kd - empirically determined coefficient. It depends on condition of the
atmosphere and time of the year.
Ba- ratio between diffuse solar radiation and total solar radiation:
Ba =0,5* (1 + cos ΘZ ).
Formula 32 /2/
τAA - transmission coefficient, determine absorption of solar radiation by aerosol
particles:
τAA =1- Kdif, * (1 - M*i + M*i1,06)* (1- τA),
Formula 33 /2/
where Kdif, =0,1.
τAS - transmission coefficient, determine deffusion of solar radiation by aerosol
particles:
18
τAS = τA / τAA.
Formula 34 /2/
Total solar radiation
Density of total solar radiation at clear atmosphere can be calculated:
Etotalhor= ( Edirecthor + Ediffusehor ) / (1 - re * ra ),
Formula 35 /2/
where re –albedo of earth surface, ra- albedo of atmosphere:
ra = 0,0685 + (1- Ba)* (1 - τAS).
Formula 35 /2/
2.3. Influence of climate factors.
Next group of factors which influence on solar radiation is climatic factors. It
includes real weather conditions (clouds, rains, haziness ), anthropogenic pollution
(impacts of different factories, traffic ). All of these factors have unpredictable
character and can be modeled only by difficult probabilistic models and prognosis. At
certain time for correct designing solar systems detail initial data of solar radiation per
many years is needed. These values at real weather conditions are registered by special
equipment. These values are published in climatologically reference book for region;
specialized atlas of solar radiation; archives and electronic data bases./3/
19
3. Example of calculation.
Initial data:
Site of interest is Tyumen city, Russia.
φM = 570 09/ - geographical latitude,
λM = 650 32/ - geographical longitude,
λav= 600 - geographical longitude of middle meridian of given time zone,
Δtleg =1 hour - correction of legal time during winter time,
Δtleg =2 hours - correction of legal time during winter time.
k ωs = 150/ hour. - coefficient of conversation of solar-hour angle into degrees
Number of
month
1
2
3
4
5
6
7
8
9
10
11
12
Date
15
15
15
15
15
15
15
15
15
15
15
15
Day
number, n
15
46
74
105
135
166
196
227
258
288
319
349
Table 1. Initial data.
Example of calculation for first month, 15 of January:
Calculation of solar inclination:
δn=23,5 * sin ( 3600 * ( n-81) / 365) = 23,5 * sin ( 3600 * ( 15-81) / 365)= -21,310.
Calculation of time correction:
B = 3600 * ( n - 1 ) / 365 = 3600 * ( 15 - 1 ) / 365 = 0,240.
20
ttime = 229,2 * ( 0,000075 + 0,001868 * cos 0,240 - 0,032077 * sin 0,240 – 0,014615
*cos 2*0,240 – 0,04089 * sin 2*0,240 = -8,63 min.
Calculation of sunset time:
tMsunset = 1 / k ωs * ( arcos(- tg
φM * tg δn ) + ( λM – λav ) ) + Δtleg - ttime +12=
=1 / 150/ h * (arcos (-tg570 09/) * tg (-21,310)) + (650 32/ – 600) ) +1 -(-8,63/60)
+12=17,11h p.m.
Calculation of daylight hours:
Ts = 2 k ωs * arcos (- tg
φM * tg δn ) = 2 * 150/ h *arcos (-tg570 09/* tg (-21,310)) =7,09 h.
Calculation of sunrise time:
tssunrise = tssunset - Ts = 17,11 h - 7,09 h = 10,02 h.
Results for other months are shown at the table 2 and figure 5.
Figure 5. Daylight hours for different month.
21
Month
January February March
April
May
June
July
August
September October November December
Number of
month
1
2
3
4
5
6
7
8
9
10
11
12
Date
15
15
15
15
15
15
15
15
15
15
15
15
Day number
15
46
74
105
135
166
196
227
258
288
319
349
Angle of solar
declination
-21,3
-13,3
-2,8
9,4
18,8
23,4
21,6
13,8
2,3
-9,6
-19,2
-23,4
t time , min
-8,6
-14,3
-9,7
-0,3
3,9
0,0
-5,8
-4,9
4,6
14,4
15,2
5,0
tMsunset, h
17,1
18,2
19,2
21,4
22,5
23,3
23,1
22,0
20,5
19,1
17,0
16,6
TS, h
7,1
9,2
11,4
14,0
16,2
17,6
17,0
15,0
12,5
10,0
7,7
6,4
tMsunrise, h
10,0
9,0
7,8
7,4
6,2
5,7
6,1
7,0
8,0
9,1
9,3
10,1
MJ/m 2
4,54
9,46
17,68
28,52
37,72
42,46
40,54
32,72
22,09
12,21
5,51
3,11
Days in month
31
28
31
30
31
30
31
31
30
31
30
31
W hor /month,
MJ/m 2
140,74
264,88
548,08
855,60
662,70
378,51
165,30
96,41
W ohor /day,
1169,32 1273,80 1256,74 1014,32
Table 2. Calculation of flux of solar radiation per month for Tyumen city, Russia.
22
Calculation of solar-hour angle for 12 o’clock:
ωs = k ωs * ( tM - Δtleg + ttime – 12) + ( λM – λav ) =
=150/ h* ( 12 – 1 + (-8,6) -12 ) + (650 32/ – 600) = -260 66/
Calculation of cosine of angle of sight on the horizontal plane:
cos ΘZ= cos δn * cos
φM * cos ωs + sin δn * sin φM =
= cos (-21,310) * cos 570 09/ * cos (-260 66/ )+ sin (-21,310) * sin 570 09/ = 0,15
Calculation of density of radiation on the horizontal plane:
E0hor= ES┴ * cos ΘZ = 1367W/m2 * 0,15 = 201 W/m2
Results for all day are shown at the table 3:
Time of the
day
ωs
cos ΘZ
E0hor
10,0
-56,43
-
0,00
11
-41,66
0,07
99,75
12
-26,66
0,15
201,00
13
-11,66
0,19
260,17
14
3,34
0,20
273,25
15
18,34
0,18
239,33
16
33,34
0,12
160,73
17,1
49,94
-
0,00
Table 3. Density of solar radiation on horizontal surface
per every hour on 15 of January.
Results for other month are shown at the Appendix 1.
23
Results can be shown graphically on the figure 6:
Figure 6. Density of solar radiation on horizontal surface
on 15 of December, on 15 of March, on 15 of July.
Calculation of flux of solar radiation per one day in the way of absolutely transparent
atmosphere or without atmosphere are done using Mathcad program:
W ohor 
t sunset
s
E o (t )  dt  4,54MJ / m 2

hor
t sunrise
s
Calculation of flux of solar radiation per month:
*N
 4,54MJ / m 2 * 31  140,74MJ / m 2 .
W hor  W o
hor
month
Results of calculation of flux of solar radiation for other month are shown at
the table 2 and figure 7:
24
Figure 7. Flux of solar radiation on horizontal surface
per month in the way of absolutely transparent atmosphere or without atmosphere.
Calculations of solar radiation in real conditions for day of every month are done using
Microsoft Office Excel. Process of calculations is shown in appendix 1.
At this example there is no opportunity to calculate real values of influence of climate
factors. Climatologically reference books for every Russian region are were
established in year 1954 in printed version only. Information from electronic data
bases of solar radiation is not free. That is why in further calculations total solar
energy is decreased on 40% because of climatic factors. /1/
Calculation of flux of direct solar radiation per one day of every month and per every
month with atmosphere and real climatic conditions are done using Mathcad program.
Results of calculations are shown at figure 8 and table 4.
25
Figure 8. Flux of solar radiation on horizontal surface
per month with atmosphere and real climatic conditions.
26
Month
January February March
April
May
June
July
August
September October November December
Wdirecthor/day,
MJ/m 2
0,04
1,08
5,19
12,55
19,14
22,47
21,14
15,58
8,00
2,21
0,15
0,01
Wdiffusehor/day,
MJ/m 2
2,06
4,36
6,81
9,05
10,72
11,65
11,06
9,8
7,63
5,15
2,67
1,5
Wtotalhor/day,
MJ/m 2
2,22
5,75
12,33
22,07
30,44
34,76
32,82
25,91
16,10
7,54
2,93
1,66
Wdirecthor/month,
MJ/m 2
1,24
30,24
160,89
376,50
593,34
674,10
655,34
482,98
240,00
68,51
4,50
0,31
Wdiffusehor/month,
MJ/m 2
63,86
122,08
211,11
271,50
332,32
349,50
342,86
303,80
228,90
159,65
80,10
46,50
Wtotalhor/month,
MJ/m 2
68,82
161,00
382,23
662,10
943,64
1042,80 1017,42
803,21
483,00
233,74
87,90
51,46
Whor/month,
MJ/m 2
41,29
96,60
229,34
397,26
566,18
625,68
481,93
289,80
140,24
52,74
30,88
610,45
Table 4. Calculation of flux of solar radiation on horizontal surface
27
per month with atmosphere and real climatic conditions for Tyumen city, Russia.
28
4. Heating demand of one family house in Tyumen, Russia.
Site of interest is a one family house which is situated in Tyumen, Russia.
Living area is about 600 m2. Walls are made of calcium-silicate bricks. Calculations
are given for the year 2008. This building is heated by two natural gas boilers. Indoor
temperature is 18 oC.
4.1. Calculation of heating demand according to thermotechnical
calculation.
Initial data:
tin=21 oC – indoor air temperature;
tout= -38 oC – outdoor designing temperature in Tyumen;
uw=0,54 W/(oC*m2) - thermal conductivity of wall (thickness is 770mm) made of
calcium-silicate bricks;
uwindow=1,3 W/(oC*m2) - thermal conductivity of window;
ufloor=0,22 W/(oC*m2) - thermal conductivity of floor;
uroof=0,11 W/(oC*m2) - thermal conductivity of roof.
Ai - total areas of walls, windows, floor, and roof.
zht = 225days. - duration of heating period;
tav = -7,2 °С - average outdoor temperature for heating period;
n=0,5(1/h) –air change ratio;
V=1800m3- volume of the building.
29
Calculation:
1) Losses through building envelope:
Degree days Dd is calculated with formula:
Dd = ( tin - tav ) zht
Formula 36 /4/
Annual energy losses through the building envelope can be calculated:
Q=Hcond*( tin - tav)*Δt = ∑Hcond * Dd ,
Formula 37/4/
Where Δt is time of heating period,
Hcond - average heat loss of a building components can be calculated by evacuation:
Hcond = Φ / ( tin - tout) ,
Formula 38 /4/
Where Φ – total heat load of the building:
Φ = ∑Hi * ( tin – tout) = ∑(ui*Ai) * ( tin – tout).
Formula 39 /4/
A - total areas of walls, windows, floor, and roof are calculated approximately
according building plan.
Results of total heat load calculation are shown in table 5:
u-value,
o
Indoor
2
W/( C*m ) A, m
2
o
o
Outdoor
H, W/ C
tin, C
tout, oC
Φ,W
wall (west)
0,38
165
89,10
18
-38
3511,2
wall (south)
0,38
165
89,10
18
-38
3511,2
wall (east)
0,38
165
89,10
18
-38
3511,2
wall (nourth)
0,38
165
89,10
18
-38
3511,2
windows
1,3
52,15
39,63
18
-38
2686,8
30
roof
0,11
600
66,00
18
-38
3696,0
floor
0,22
300
66,00
18
6
792,0
Total
21219,6
Table 5. Heat load through building envelope of one family house in Tyumen, Russia.
Average heat loss of a building components can be calculated:
Hcond = 21219,6 W / ( 18 oC – (-38 oC)) = 454,7 W/ oC.
Degree days Dd is according (formula 36):
Dd = (18°С – ( -7,2°С)) · 225 days = 5670°С·day
Annual energy losses through the building envelope according (formula 37):
Q=454,7 W/ oC *5670°С·day *24 h= 61876 kWh =61,9 MWh.
2) Heating demand for HDW:
Total cold water demand is measured by water meter. It is 111000 liters. Hot water
consumption is about 1/3 of total demand. It is 37000 liters. Heat demand which is
needed to heat this amount of water can be calculated:
Q = Vwater*ρ* cp* ( thot – tcold)
Formula 40
Q = 37000 l*1 l/kg* 4,2 kJ/(kg°С) * ( 60°С – 5°С) = 8567 MJ=2,4 MWh.
31
3) Heat load from ventilation:
Q = V* n*ρ* cp* ( tsupply– toutdoor)*τ
Calculations for heat load of ventilation are given at table 6. Average temperatures
for every month are taken from “Building rules and norms of Russian Federation”
(Building climatology)
Number of
month
I
II
III
IV
V
VI
VII
VIII
IX
X
XI
XII
Average
outdoor
temperature,
°С
-17,4
-16,1
-7,7
3,2
11
15,7
18,2
14,8
9,7
1
-7,9
-13,7
31
28
31
30
31
30
31
31
30
31
30
Heat load,
kW
9,0
8,7
6,6
3,8
1,8
0,6 -0,1
0,8
2,1
4,3
6,6
8,1
Energy
consumption,
MWh
6,7
5,8
4,9
2,7
1,3
0,4
0,6
1,5
3,2
4,8
6,0
Days in month
0,0
Table 6. Heat load of ventilation for one family house in Tyumen, Russia.
Total energy demand is 102,3 MWh per year.
Total
31
38,0
32
4.2. Calculation of heating demand according to the gas consumption.
Initial data:
Specific combustion heat of natural gas is taken 28MJ/m3.
Price of the natural gas is 2,15 rub/m3. (0,05 €/m3)
Euro rate 43,2 rub.
Volume consumption of natural gas is taken from bills for year 2008.
Total energy consumption and costs of fuel are given in table 5:
Energy
Consumption
of gas, m3
MJ
MWh
Month
consumption
Cost of
Cost of
for heating,
gas, rub
gas, €
MWh
January
2247
62916
17,48
15,77
4831,05
111,83 €
February
2967
83076
23,08
21,37
6379,05
147,66 €
March
1368
38304
10,64
8,93
2941,2
68,08 €
April
1328
37184
10,33
8,62
2855,2
66,09 €
May
927
25956
7,21
5,50
1993,05
46,14 €
June
220
6160
1,71
0,00
473
10,95 €
July
220
6160
1,71
0,00
473
10,95 €
August
220
6160
1,71
0,00
473
10,95 €
September
500
14000
3,89
2,18
1075
24,88 €
33
October
1300
36400
10,11
8,40
2795
64,70 €
November
1665
46620
12,95
11,24
3579,75
82,86 €
December
2300
64400
17,89
16,18
4945
114,47 €
Total:
15262
427336
118,70
98,17
32813,3
759,57 €
Table 5. Total energy consumption and costs of fuel for
one family house in Tyumen, Russia.
4.3. Total energy demand for heating and HDW
Calculated values of energy demand are not the same. It takes place because:

Designing U-values of the materials are not realistic;

Heat losses of ventilation are approximated;

Heat losses of heating systems are not calculated;

Heat losses of leakage air are not taken into account.
At further calculations calculation of energy demand according gas
consumption must be used. This calculation is more accurate.
At summer period during June, July and August there is no need of heating. All
energy is used for hot domestic water. So, energy consumption for hot domestic water
is 1,71 MWh per month.
Total energy demand for heating and HDW per every month is shown on the
figure 9:
34
Figure 9. Total energy demand for heating and HDW per every month
for one family house in Tyumen, Russia
35
5. Usage of solar energy.
5.1. Solar house
Last 15-20 years “solar” houses have become more and more popular. The simplest
way is to use solar energy for heating and lighting. In this way the biggest part of
energy demand is provide by solar energy. Well designed “solar” house with effective
solar heating system can totally meet the demands of heat and light, even without other
sources of energy. There will be no need of district system connection, of meters, and
storages for fuel.
Main goals of “solar” house are:
 to maximize utilization of solar radiation;
 to transfer solar energy into heat and electricity;
 to store solar energy in the house with minimum of energy losses.
If these goals are achieved, considerable amount of money can be saved. Ecological
situation will be better. Because of reducing of usage of other energy sources amount
of combustion products (which are dispersed to the atmosphere) becomes lower, roads
will be free of heavy transport of million tons of fuel, forests will be saved.
There are two types of energy saving systems for “solar” house:
1. Passive
2. Active
First is based on architectural and constructional methods. For example, house is
orientated in axes south-north; there is no shade on the southern wall; minimum of
windows on the northern wall; southern wall is a window wall; two or three-glass
cover; reinforced thermo-insulation of walls; wind-porches, etc.
36
“Passive solar design systems usually have one of three designs:

Direct gain (the simplest system) stores and slowly releases heat energy
collected from the sun shining directly into the building and warming materials
such as tile or concrete. Care must be taken to avoid overheating the space.

Indirect gain (similar to direct gain) uses materials that hold, store, and release
heat; the material is located between the sun and living space (typically the
wall).

Isolated gain collects solar energy remote from the location of the primary
living area. For example, a sunroom attached to a house collects warmer air
that flows naturally to the rest of the house. “ /5/
This technical method increases costs of construction by 5-10%. But it reduce 50% of
costs of heating.
Active solar energy saving system consists of solar collectors, solar batteries,
equipment for control, computer and other high-performance equipment for maximal
using of solar energy.
There are two basic active ways of transforming solar energy:

Thermal

Photovoltaic
First is simpler. Heat-transfer agent (usually it is water) is heated in the collector
(system of tubes, which are collecting and absorbing solar energy). It has high
temperature and can be used for heating in buildings. Collector is installed on the roof
of the building. Position is chosen to get more energy per day. Part of solar radiation is
accumulated in water tanks to provide heat when the sun is not shining.
Solar photovoltaics (PVs) are arrays of cells containing a material that converts solar
radiation directly into electricity current. Materials presently used for photovoltaics
37
include amorphous silicon, polycrystalline silicon, microcrystalline silicon, cadmium
telluride, and copper indium selenide/sulfide.
There are many “solar” houses in the world. They can totally or partially be provided
by solar energy. They are built not only in southern countries like Egypt, Israel,
Turkey, Japan, India, USA. Many countries with moderate climate (France, England,
Germany) and northern countries like Sweden, Finland, Canada use solar energy too.
Specialized companies produce the equipment and materials for “solar” houses. Big
concerns like Concept Construction (Canada) and Enercon Building Corporation
(USA) are involved in a building process.
5.2. Types of solar collectors
Solar collectors transform solar radiation into heat and transfer that heat to a medium
(water, solar fluid, or air). Then solar heat can be used for heating water, to back up
heating systems or for heating swimming pools.
Flat plate collector
Plate collectors (Figure 10) consist of elements, which absorb solar radiation,
transparent covering and insulated layer. Absorbing layer is called absorber. It is
connected to heat distribution system. Transparent element (glass) usually is made of
prestressed glass where content of metals is reduced. Flat plate collectors can heat
water till 190-200°C.
Efficiency of collector depends on amount of solar energy, which is transformed to a
medium. The efficiency can be increased using special optic coverings, which don’t
radiate heat. Standard decision for increasing efficiency is to use absorber made of flat
copper.
38
Figure 10. Flat plate collector./6/
Evacuated tube collector
These collectors (Figure 11) can heat water till 250-300°C. It happens because heat
losses are reduced by multilayer glassing coating and vacuum inside collector.
Principe of evacuated tube collector is the same as thermos. External part of the tube is
transparent. Internal plates have highly selective covering which detect solar energy.
Vacuum is inside the tube. Vacuum layer is a heat-insulating layer and it gives an
opportunity to save 95% of detected solar energy.
Heat pipes with absorber plates (which are inside the glass tube) are thermal
conductors. Liquid in these pipes is vaporized. It condensed in the highest part of the
tube and transfer heat to the collector.
The highest efficiency can be achieved (in comparison with other types of collectors)
in low temperature conditions and low flux of solar radiation.
39
Figure 11. Evacuated tube collector./6/
Concentrating collectors
These collectors (Figure 12) can heat water till 120-250°C. It is due to using
concentration of solar energy. Cylindrical parabolic concentrators are under absorbing
elements. To achieve highest efficiency solar tracer is needed.
40
Figure 12. Concentrating collector./6/
Which collector is suitable for which situation?
The desired temperature range of the material to be heated is the most important factor
in choosing the correct type of collector. An uncovered absorber is certainly not
suitable for producing process heat. The amount of radiation on that spot, exposure to
storms, and the amount of space must all be carefully considered when planning a
solar array.
Graph of efficiency and temperature ranges of various types of collectors is shown at
figure 13:
41
Figure 13. Graph of efficiency and temperature ranges of various
types of collectors (radiation: 1000 W/m²)/6/
5.3. Types of solar water heating systems
All the active solar water heating systems are divided in two general categories: open
loop systems and closed loop systems.
Open Loop Systems (figure 14)
These are basic type of systems. They are simple and appeared long time ago. The
main principle of the open loop system is the water circulating directly through the
solar collectors and then returns to the storage tank. There is special pump controller
which is called differential controller. It turns the pump on when collectors have higher
temperature than stored water and shut is off when they get the same temperature. This
type of system has several benefits such as low cost and easy installation. On the other
hand there are significant drawbacks:
1. No totally reliable form of freeze protection
42
Collectors are drained manually so they can be set only in areas which
never freeze
2. No high limit protection
There is possibility that water in the storage tank and solar collector can
boil if there won’t be daily consumption of hot water
3. In areas of waste water the solar collectors are sensitive to clogging from
mineral deposits
Figure 14. Open loop solar water heating system./7/
Closed Loop Systems
In closed loop system water doesn’t circulate directly through the solar collectors.
There is special fluid which is separated and circulates through the collectors. Then it
goes to heat exchanger which transfers the heat to the water in storage tank. This fluid
is often propylene glycol. There is special equipment in closed loop systems such as an
expansion tank, pressure gages and fill valves.
43
There are two types of closed loop systems:
1) Glycol Indirect System is shown on the figure 15.
Figure 15. Glycol Indirect solar water heating system./7/
It is used for a long time like the open loop system but with a mixture of
glycol and water as the heat transfer fluid the problem of freezing is
removed. Nevertheless there are problems of high limit protection and the
possibility of failure of the added components such as expansion tank or
pressure gages.
2) Drainback system (figure 16)
This type of system is non-pressurized and uses water as a heat transfer
fluid. The solution is a small drainback reservoir which is installed in the
collector loop which is located lower than collectors. That is why water
reaches only the top of reservoir and collectors stay dry when the pump
doesn’t work. Pump circulates water in the reservoir through the collectors
44
where it is heated when collectors are hotter than the water in storage. Also
there is a heat exchanger which transfers heat from this water to the heat
storage tank. The pump shuts off when collectors reach the same
temperature as the water in the storage tank or this water gets a preset
temperature. Then all the water drains back to the reservoir. This type of
system has several benefits:

freeze protection is based on gravity

damage of collectors in hard water areas is almost eliminated

less components which can failure
Figure 16. Drainback solar water heating system./7/
45
5.4. The operating principle of solar water heating system
Figure 17. Solar water heating system./8/
Basic working principle of solar water heating system is shown in figure 17. The main
idea is to maintain maximum temperature difference between heat exchanger and
heated water. Efficiency increases when temperature difference is as high as possible.
So, solar heat exchanger must be in the coldest place. Cold water is at the lower part of
the storage tank. Stratification of water with different temperature (from lowest to
highest) is due to gravity. Density of cold water is more than density of hot water.
All connections are carried out in this way to prevent mixing of cold and hot water.
Hot domestic water is taken from the highest point, where temperature is high enough.
Incoming cold water connection is situated in the lowest place, near solar heat
exchanger. Water temperature for heating purposes is taken from highest point (where
46
temperature is near 80°C.) Returned water connection is in the middle of the tank,
where temperature is the same as returned water temperature.
Solar storage tank should be high enough to maintain temperature difference inside. In
other case gravity principle will not work. Sometimes thermostable panels are made
inside the tank to make a tunnel for water. It helps to prevent water mixing.
When solar energy is not enough oil or gas boiler starts to work. But it must not reduce
solar energy efficiency. That is why it is connected upper than solar heat exchanger.
47
6. Summary
Values of solar energy are very low for winter period. That is why it is decided to use
solar energy only for hot domestic water in summer period. Evacuated tube collector is
chosen for a system as the most effective. It can transfer into heat more than 95% of
incoming solar energy. Potential consumption of solar energy is taken from previous
calculations of solar radiation on horizontal surface per month with atmosphere and
real climatic conditions. Solar collector where area is 10m2 will be enough to provide
heat for DHW in summer months. As shown in figure 18.
Figure 18. Quantity of solar energy in total energy demand.
Calculation of cost efficiency
Discount cash model is used for cost efficiency calculation.
All amounts of money are corrected with discount factor:
D=1/(1+i)n
where D – discount factor;
i - interest rate;
n - number of the period.
Formula 41 /9/
48
1. Net present value - NPV
2. Payback period - PB
3. Internal rate of return - IRR
4. Profitability index - PI
1. NPV (Net Present Value)
NPV 
t2
t2
n  t1
n  t1
 DInflow   DOutflow
Formula 42 /9/
where:
n-number of the period;
t1, t2-interval of calculations.
When NPV is negative project is not cost efficient.
2. PP (Payback Period)
During Payback Period all investment costs must be compensated.
t2
t2
n  t1
n  t1
 DInflow   DOutflow  0
Formula 43 /9/
where:
n – number of the period of the project;
t1, t2 - interval of calculations;
D – discount factor.
3. IRR (Internal Rate of Return)
IRR shows maximum investment cost. For example, maximum interest on credit,
which can be taken for a project.
t2
Inflow(a) t 2 Outflow(a)
0
 IRR   n
IRR 
n  t1 
 t1 
1 

1 

 100 
 100 
where:
n - number of the period of the project;
Formula 44 /9/
49
t1, t2 - interval of calculations;
D – discount factor.
4. PI (Profitability Index)
Profitability Index shows net profit per unit of investment.
PI = NPV / I
Formula 45 /9/
where:
NPV – Net Present Value;
I - investment.
At this example minimum investment cost of equipment is 90000rub (price is given for
year 2009). Minimum operation life of the solar heating system is 20 years.
Inflation in Russia is 14% for year 2009./10/
Interest on credit in Sberbank of Russian Federation is 18%./10/
Rise of gas price at internal market is expected 30%./10/
Calculations of cost efficiency are made in Excel program. Process of calculations is
shown at table 6.
Results of calculations are:
PP=14,41 year;
IRR=47,02%;
PI=3,33.
Project is cost efficient.
50
Number of the year
Return, because of using solar
energy
Deprecation
Credit payment
Inflow
NPV(14%)
NPV(60%)
Number of the year
Return, because of using solar
energy
Deprecation
Credit payment
Inflow
NPV(14%)
NPV(60%)
1
2
3493,1
4500
5310
2683
2065
1048
3
4541,0
3
4500
5310
3731
2518
911
4
5903,33
9
4500
5310
5093
3016
777
5
7674,3
41
4500
5310
6864
3565
655
6
9976,6
43
4500
5310
9167
4176
546
7
12969,
64
4500
5310
12160
4859
453
8
16860,
53
4500
5310
16051
5627
374
9
21918,
68
4500
5310
21109
6491
307
10
28494,
29
4500
5310
27684
7468
252
2687
4500
5310
1877
1646
1173
11
3704
2
4500
5310
3623
3
8573
206
12
48155,
35
4500
5310
13
62601,
95
4500
5310
14
81382,5
4
4500
5310
15
105797
,3
4500
5310
16
137536
,5
4500
5310
17
178797
,4
4500
5310
18
232436
,7
4500
5310
19
302167
,7
4500
5310
20
392818
4500
5310
47345
9827
168
61792
11250
137
80573
12868
112
104987
14708
91
136726
16803
74
177987
19187
60
231627
21903
49
301358
24997
40
392008
28523
32
Table 6. Indexes of efficiency of investment project.
51
Conclusion
Solar water heating systems can be used effectively in cold climate conditions during
6-7 month per year (March/April-September) for domestic hot water, underfloor
heating or space heating.
However, solar energy is not very popular in Russia. It has many problems, such as:

There is no big experience in building solar systems;

Inclement climate;

Climatology data bases are rather old;

Ratio between cost of solar collectors and it’s efficiency is not high enough;

No solar heating association is needed to cooperate with other countries.
Lack of solar radiation is the problem of northern regions. Sometimes even solar
collector with large area can not be enough to provide required energy demand. In this
case designers must think how to decrease heating demand. This aim could be
achieved due to decrease heat losses through building envelope. Passive solar heating
should be taken into account at the design phase. Different ways of accumulating
energy must be used in buildings.
Investment cost of equipment which transformed solar energy looks to high in
comparison with cost of natural gas or light oil. Cost efficiency of this project is not
high in conditions of Russian economics. It is due to high level of interest of credit. In
given example project is cost efficient. It is no difference for customer to pay for fuel
or invest money into solar heating system. Sometimes it is not cost-beneficial to use
solar systems, but we must think in perspective way. Fossil fuels are not renewable.
New sources of energy must be improved.
52
However fossil fuel usage has a great influence on the ecology of our planet. And it is
an irreversible process. In my view it is governmental problem, so government must
stimulate customers to use environmentally-friendly systems for their houses. Our
nature needs to be protected by government and by each person.
53
Bibliography
1. Elistratov V.2009. Solar power plants. Valuation of solar radiation.(Солнечные
энергоустановки. Оценка поступления солнечного излучения.) Saint-Petersburg.
Polytechnic University.
2.Bird, Richard 1981. A simplified clear sky model for direct and diffuse insolation on
horizontal surfaces. Colorado. Solar Energy Research Institute.
3. Russian Federal Service for Hydrometeorology and Environmental Monitoring
1964-2007 data. World radiation data centre (WRDC) online archive. [ referred
11.02.2010] Available in www-format: <http://wrdc.mgo.rssi.ru/>
4. Building climatology. (СНиП 23-01-99 Строительная климатология.) 1999.
Building rules and norms of Russian Federation.
5.U.S. Energy Efficiency and Renewable Energy. Solar Energy Technologies
Program. Department of Energy. Available in www-format:
<http://www1.eere.energy.gov/solar/sh_basics_space.html>
6. Solar Collectors: Different Types and Fields of Application BINE Information
Service. Bonn, Germany. Fachinformationszentrum (FIZ). [referred 11.02.2010]
Available in www-format: <http://www.solarserver.de/wissen/sonnenkollektorene.html>
7. Solar hot water basics 2007. New Mexico Solar Energy Association. [referred
11.02.2010] Available in www-format:
<http://www.freenergy.casadelstarkey.com/index.php?module=pagemaster&PAGE_us
er_op=view_page&PAGE_id=4&MMN_position=10:8>
8. Solar water heating system. [referred 11.02.2010] Available in pdf-format: <
http://www.my-dna.it/download/suntek/solvis/SOLVISMAX%20Pamphlet_2006.pdf>
54
9. Indexes of efficiency of investment project. [referred 11.02.2010] Available in
www-format: <http://www.investplans.ru/index.php/business-planning-info/npv-irretc.html>
10.Sberbank [on line] Moscow.[referred 11.02.2010] Available in www-format:
<http://www.sbrf.ru/moscow/>
55
Appendix
Janyary
Time
of the
day
10,0
11
12
13
14
15
16
17,1
ωc
cos θz
-56,43
-41,66 0,07
-26,66 0,15
-11,66 0,19
3,34
0,20
18,34 0,18
33,34 0,12
49,94
-
February
Time
of the
day
ωc
9,02
10,00
11,00
12,00
72,72
58,07
43,07
-
Ehor
Mi
trayleigh taerosol tozone tgas
TH2O Edirect B
taa
tas
Ediffuse ra
0,00
99,75 13,70
0,00
-0,29
0,99
0,98
0,80
0,00
0,54
0,57 -0,52
34,64
0,77
201,00
6,80
0,00
0,45
0,99
0,98
0,82
0,23
0,57
0,90
0,50
94,00
0,28
260,17
5,25
0,01
0,59
0,99
0,98
0,83
3,52
0,60
0,94
0,63
125,43
0,22
273,25
5,00
0,02
0,61
0,99
0,98
0,83
5,25
0,60
0,94
0,65
131,88
0,21
239,33
5,71
0,01
0,55
0,99
0,98
0,83
1,65
0,59
0,93
0,59
114,73
0,24
160,73
8,50
0,00
0,29
0,99
0,98
0,81
0,01
0,56
0,85
0,34
71,23
0,36
0,00
-
cos θz Ehor
Mi
trayleigh taerosol tozone tgas
-
0,00
-
-
0,09
118,11
11,57
0,00
0,19
0,27
263,60
373,15
5,19
3,66
0,02
0,11
-
TH2O Edirect B
taa
tas
Ediffuse ra
-
-
-
-
-
-
-
-
-0,04
0,99
0,98
0,81
0,00
0,54
0,71
-0,05
46,06
0,59
0,72
0,99
0,99
0,98
0,98
0,83
0,84
3,93
36,78
0,60
0,64
0,94
0,96
0,63
0,74
127,14
172,52
Etot
40,
99,
134,
143,
122,
76,
-
Etot
0,55
-
51,7
0,22 137,0
0,16 216,2
56
13,00
14,00
15,00
16,00
17,00
18,00
18,18
28,07
13,07
1,93
16,93
31,93
46,93
61,93
64,69
March
Time
of the
day
7,79
8,00
9,00
10,00
11,00
12,00
13,00
14,00
15,00
16,00
17,00
ωc
cos θz
-89,99
-86,91
-71,91 0,13
-56,91 0,25
-41,91 0,36
-26,91 0,44
-11,91 0,49
3,09
0,50
18,09 0,47
33,09 0,41
48,09 0,32
0,32
0,33
0,31
0,26
0,17
0,06
-
439,30
457,57
426,70
348,79
229,15
75,92
0,00
3,11
2,99
3,20
3,92
5,97
18,01
-
0,18
0,20
0,17
0,08
0,01
0,00
-
0,76
0,77
0,75
0,70
0,52
-0,90
-
1,00
1,00
1,00
0,99
0,99
0,98
-
0,98
0,98
0,98
0,98
0,98
0,97
-
0,85
0,85
0,84
0,84
0,83
0,79
-
75,59
88,40
67,24
25,95
1,07
0,00
-
0,66
0,67
0,66
0,63
0,58
0,53
-
0,97
0,97
0,97
0,96
0,92
0,16
-
0,78
0,79
0,78
0,73
0,57
-5,53
-
190,84
194,86
187,82
164,10
109,34
18,67
-
0,14
0,14
0,15
0,17
0,25
3,15
-
274,2
291,3
262,7
196,7
116,1
50,5
-
Ehor
Mi
trayleigh taerosol tozone tgas
TH2O Edirect B
taa
tas
Ediffuse ra
0,00
0,00
174,04
7,85
0,00
0,35
0,99
0,98
0,82
0,03
0,56
0,87
0,40
78,85
0,33
348,42
3,92
0,08
0,70
0,99
0,98
0,84
25,80
0,63
0,96
0,73
163,96
0,17
495,23
2,76
0,25
0,79
1,00
0,98
0,85 117,18
0,68
0,98
0,81
201,97
0,13
604,48
2,26
0,37
0,83
1,00
0,98
0,85 213,98
0,72
0,98
0,84
215,70
0,11
668,73
2,04
0,43
0,84
1,00
0,98
0,86 276,98
0,74
0,98
0,86
220,54
0,11
683,60
2,00
0,44
0,85
1,00
0,98
0,86 291,99
0,75
0,98
0,86
221,43
0,10
648,09
2,11
0,41
0,84
1,00
0,98
0,86 256,39
0,74
0,98
0,85
219,17
0,11
564,60
2,42
0,33
0,81
1,00
0,98
0,85 176,80
0,71
0,98
0,83
211,66
0,12
438,83
3,12
0,18
0,76
1,00
0,98
0,85
75,27
0,66
0,97
0,78
190,73
0,14
Etot
84,4
196,4
327,6
439,5
508,2
524,2
486,0
397,8
273,8
57
18,00
19,00
19,2
63,09
78,09
81,40
0,20
0,07
-
April
Time
of the
day
7,38
8,00
9,00
10,00
11,00
12,00
13,00
14,00
15,00
16,00
17,00
18,00
19,00
20,00
21,00
21,4
ωc
cos θz
-93,89
-84,56 0,19
-69,56 0,32
-54,56 0,45
-39,56 0,55
-24,56 0,62
-9,56
0,67
5,44
0,67
20,44
0,64
35,44
0,57
50,44
0,48
65,44
0,36
80,44
0,23
95,44
0,09
110,44
115,80
-
279,34
96,98
0,00
4,89
14,10
-
0,02
0,00
-
0,62
-0,34
-
0,99
0,98
-
0,98
0,98
-
0,83
0,80
-
6,23
0,00
-
0,60
0,54
-
0,94
0,54
-
0,65
-0,64
-
134,80
32,86
-
0,21 147,1
0,83 39,3
-
Ehor
Mi
trayleigh taerosol tozone tgas
TH2O Edirect B
taa
tas
Ediffuse ra
0,00
257,93
5,30
0,01
0,58
0,99
0,98
0,83
3,27
0,59
0,93
0,62
124,30
0,22
444,06
3,08
0,19
0,76
1,00
0,98
0,85
78,85
0,66
0,97
0,79
191,93
0,14
612,77
2,23
0,38
0,83
1,00
0,98
0,85 221,91
0,72
0,98
0,84
216,43
0,11
752,56
1,82
0,50
0,86
1,00
0,99
0,86 363,07
0,78
0,98
0,87
224,71
0,10
853,91
1,60
0,57
0,88
1,00
0,99
0,86 470,53
0,81
0,99
0,89
227,80
0,09
909,93
1,50
0,60
0,88
1,00
0,99
0,87 530,82
0,83
0,99
0,89
228,98
0,09
916,80
1,49
0,60
0,88
1,00
0,99
0,87 538,24
0,84
0,99
0,89
229,11
0,09
874,06
1,56
0,58
0,88
1,00
0,99
0,87 492,16
0,82
0,99
0,89
228,26
0,09
784,61
1,74
0,52
0,86
1,00
0,99
0,86 396,75
0,79
0,99
0,88
225,86
0,09
654,54
2,09
0,42
0,84
1,00
0,98
0,86 262,80
0,74
0,98
0,85
219,62
0,11
492,71
2,77
0,25
0,79
1,00
0,98
0,85 115,16
0,68
0,97
0,81
201,54
0,13
310,14
4,41
0,04
0,66
0,99
0,98
0,83
12,94
0,61
0,95
0,69
148,75
0,19
119,26 11,46
0,00
-0,02
0,99
0,98
0,81
0,00
0,54
0,71 -0,03
46,76
0,54
0,00
0,00
-
Etot
133,4
278,6
448,3
599,4
711,0
773,1
780,7
733,3
634,6
492,9
325,1
168,0
52,4
-
58
May
Time
of the
day
ωc
6,25
7,00
8,00
9,00
10,00
11,00
12,00
13,00
14,00
15,00
16,00
17,00
18,00
19,00
20,00
21,00
22,00
22,5
109,84
-98,52
-83,52
-68,52
-53,52
-38,52
-23,52
-8,52
6,48
21,48
36,48
51,48
66,48
81,48
96,48
111,48
126,48
133,50
June
cos θz Ehor
0,20
0,33
0,46
0,58
0,67
0,74
0,78
0,78
0,75
0,68
0,59
0,48
0,35
0,21
0,08
-
0,00
266,86
450,12
627,94
788,21
920,04
1014,43
1064,98
1068,22
1023,95
935,18
807,95
650,92
474,79
291,54
113,65
0,00
0,00
Mi
5,12
3,04
2,18
1,73
1,49
1,35
1,28
1,28
1,34
1,46
1,69
2,10
2,88
4,69
12,03
-
trayleigh taerosol tozone tgas
0,02
0,20
0,39
0,53
0,61
0,65
0,67
0,67
0,66
0,61
0,54
0,42
0,23
0,03
0,00
-
0,60
0,77
0,83
0,87
0,88
0,89
0,90
0,90
0,90
0,89
0,87
0,84
0,78
0,63
-0,09
-
0,99
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
0,99
0,99
-
0,98
0,98
0,98
0,99
0,99
0,99
0,99
0,99
0,99
0,99
0,99
0,98
0,98
0,98
0,98
-
TH2O Edirect B
0,83
0,85
0,86
0,86
0,87
0,87
0,87
0,87
0,87
0,87
0,86
0,86
0,85
0,83
0,80
-
4,35
83,08
236,59
400,56
541,74
644,14
699,15
702,68
654,49
558,12
421,48
259,20
101,19
8,52
0,00
-
taa
0,60
0,66
0,73
0,79
0,84
0,87
0,89
0,89
0,87
0,84
0,80
0,74
0,67
0,61
0,54
-
0,94
0,97
0,98
0,99
0,99
0,99
0,99
0,99
0,99
0,99
0,99
0,98
0,97
0,95
0,68
-
tas
0,64
0,79
0,85
0,88
0,89
0,90
0,91
0,91
0,91
0,90
0,88
0,85
0,80
0,67
-0,13
-
Ediffuse ra
128,76
193,27
217,68
225,98
229,17
230,63
231,29
231,33
230,76
229,43
226,59
219,37
198,30
140,50
43,33
-
Etot
0,21
0,14
0,11
0,09
0,09
0,08
0,08
0,08
0,08
0,08
0,09
0,11
0,13
0,20
0,59
-
139
284
464
638
784
889
945
948
899
801
660
489
307
155
49
-
59
Time
of the
day
5,71
6,00
7,00
8,00
9,00
10,00
11,00
12,00
13,00
14,00
15,00
16,00
17,00
18,00
19,00
20,00
21,00
22,00
23,00
23,30
ωc
118,78
114,50
-99,50
-84,50
-69,50
-54,50
-39,50
-24,50
-9,50
5,50
20,50
35,50
50,50
65,50
80,50
95,50
110,50
125,50
140,50
145,00
cos θz Ehor
Mi
-
0,00
-
0,13
0,25
0,38
0,51
0,62
0,72
0,79
0,82
0,83
0,80
0,74
0,65
0,54
0,42
0,29
0,16
0,04
-
173,11
343,16
520,82
694,01
850,93
980,89
1075,06
1127,01
1133,21
1093,25
1009,83
888,64
737,94
567,97
390,31
217,06
60,01
0,00
0,00
7,90
3,98
2,62
1,97
1,61
1,39
1,27
1,21
1,21
1,25
1,35
1,54
1,85
2,41
3,50
6,30
22,78
-
trayleigh taerosol tozone tgas
0,00
0,07
0,28
0,45
0,57
0,64
0,68
0,69
0,70
0,68
0,65
0,59
0,49
0,33
0,12
0,00
0,00
-
0,35
0,69
0,80
0,85
0,87
0,89
0,90
0,90
0,90
0,90
0,89
0,88
0,86
0,81
0,73
0,49
-1,74
-
TH2O Edirect B
-
-
-
0,99
0,99
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
0,99
0,99
0,98
-
0,98
0,98
0,98
0,98
0,99
0,99
0,99
0,99
0,99
0,99
0,99
0,99
0,99
0,98
0,98
0,98
0,97
-
0,82
0,84
0,85
0,86
0,86
0,87
0,87
0,87
0,87
0,87
0,87
0,87
0,86
0,85
0,84
0,82
0,78
-
0,03
23,73
138,29
302,57
467,34
607,68
710,12
766,73
773,49
729,94
639,13
507,86
347,82
179,86
45,60
0,59
0,00
-
taa
0,56
0,63
0,69
0,75
0,81
0,86
0,89
0,91
0,91
0,90
0,87
0,83
0,77
0,71
0,64
0,58
0,52
-
0,87
0,96
0,98
0,98
0,99
0,99
0,99
0,99
0,99
0,99
0,99
0,99
0,98
0,98
0,97
0,91
-0,56
-
tas
Ediffuse ra
-
0,40
0,72
0,82
0,86
0,89
0,90
0,91
0,91
0,91
0,91
0,90
0,89
0,87
0,83
0,76
0,54
3,10
-
78,32
162,01
206,00
222,01
227,73
230,16
231,42
232,04
232,12
231,64
230,57
228,56
224,11
212,04
177,88
102,82
6,36
-
Etot
-
-
0,33
8
0,17 19
0,13 35
0,10 53
0,09 70
0,08 85
0,08 95
0,08 101
0,08 102
0,08 97
0,08 88
0,09 74
0,10 58
0,12 40
0,16 23
0,26 10
-0,94
-
60
July
Time
of the
day
6,06
7,00
8,00
9,00
10,00
11,00
12,00
13,00
14,00
15,00
16,00
17,00
18,00
19,00
20,00
21,00
22,00
23,00
23,10
ωc
115,12
100,94
-85,94
-70,94
-55,94
-40,94
-25,94
-10,94
4,06
19,06
34,06
49,06
64,06
79,06
94,06
109,06
124,06
139,06
140,56
cos θz Ehor
Mi
-
-
-
0,21
0,34
0,47
0,59
0,69
0,76
0,80
0,81
0,79
0,73
0,64
0,53
0,40
0,27
0,14
0,03
-
291,49
471,25
647,66
808,69
943,39
1042,59
1099,53
1110,35
1074,29
993,81
874,41
724,19
553,40
373,65
197,19
36,03
0,00
0,00
4,69
2,90
2,11
1,69
1,45
1,31
1,24
1,23
1,27
1,38
1,56
1,89
2,47
3,66
6,93
37,94
-
trayleigh taerosol tozone tgas
0,03
0,22
0,41
0,54
0,62
0,66
0,69
0,69
0,68
0,64
0,58
0,48
0,32
0,11
0,00
0,00
-
0,63
0,78
0,84
0,87
0,89
0,90
0,90
0,90
0,90
0,89
0,88
0,85
0,81
0,72
0,44
-6,15
-
TH2O Edirect B
-
-
-
0,99
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
0,99
0,99
0,97
-
0,98
0,98
0,98
0,99
0,99
0,99
0,99
0,99
0,99
0,99
0,99
0,99
0,98
0,98
0,98
0,97
-
0,83
0,85
0,86
0,86
0,87
0,87
0,87
0,87
0,87
0,87
0,87
0,86
0,85
0,84
0,82
0,77
-
8,51
98,51
255,97
422,26
567,01
674,77
736,79
748,57
709,29
621,72
492,54
333,57
166,69
37,03
0,18
0,00
-
taa
0,61
0,67
0,74
0,80
0,85
0,88
0,90
0,91
0,89
0,86
0,82
0,76
0,70
0,64
0,57
0,51
-
0,95
0,97
0,98
0,99
0,99
0,99
0,99
0,99
0,99
0,99
0,99
0,98
0,98
0,96
0,90
-6,33
-
tas
Ediffuse ra
-
0,67
0,80
0,85
0,88
0,90
0,91
0,91
0,91
0,91
0,90
0,89
0,87
0,83
0,74
0,49
0,97
-
140,47
197,62
219,14
226,61
229,57
231,01
231,72
231,85
231,41
230,35
228,27
223,51
210,35
172,68
91,89
-23,00
-
Etot
0,20
0,13
0,11
0,09
0,08
0,08
0,08
0,08
0,08
0,08
0,09
0,10
0,12
0,16
0,29
0,08
-
-
155
304
485
661
810
920
983
995
955
866
733
568
386
216
97
-23
-
61
August
Time
of the
day
ωc
6,98
7,00
8,00
9,00
10,00
11,00
12,00
13,00
14,00
15,00
16,00
17,00
18,00
19,00
20,00
21,00
21,95
101,06
100,73
-85,73
-70,73
-55,73
-40,73
-25,73
-10,73
4,27
19,27
34,27
49,27
64,27
79,27
94,27
109,27
123,55
cos θz Ehor
Mi
-
0,00
-
0,10
0,24
0,38
0,50
0,60
0,68
0,72
0,73
0,70
0,64
0,54
0,43
0,30
0,16
0,03
-
140,95
328,68
512,71
680,52
820,68
923,66
982,44
993,01
954,67
870,01
744,81
587,58
409,04
221,33
37,24
0,00
9,70
4,16
2,67
2,01
1,67
1,48
1,39
1,38
1,43
1,57
1,84
2,33
3,34
6,18
36,71
-
trayleigh taerosol tozone tgas
0,00
0,06
0,27
0,44
0,55
0,61
0,64
0,64
0,62
0,58
0,49
0,35
0,15
0,00
0,00
-
0,17
0,68
0,79
0,84
0,87
0,88
0,89
0,89
0,89
0,88
0,86
0,82
0,74
0,51
-5,66
-
TH2O Edirect B
-
-
-
0,99
0,99
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
0,99
0,97
-
0,98
0,98
0,98
0,98
0,99
0,99
0,99
0,99
0,99
0,99
0,99
0,98
0,98
0,98
0,97
-
0,81
0,84
0,85
0,86
0,86
0,87
0,87
0,87
0,87
0,87
0,86
0,85
0,84
0,82
0,77
-
0,00
18,53
131,47
288,87
435,02
545,66
609,36
620,85
579,23
487,81
354,98
198,01
56,26
0,74
0,00
-
taa
0,55
0,62
0,69
0,75
0,80
0,84
0,86
0,86
0,85
0,82
0,77
0,71
0,65
0,58
0,51
-
0,80
0,96
0,98
0,98
0,99
0,99
0,99
0,99
0,99
0,99
0,98
0,98
0,97
0,92
-5,57
-
tas
Ediffuse ra
-
0,21
0,71
0,81
0,86
0,88
0,90
0,90
0,90
0,90
0,89
0,87
0,84
0,77
0,55
1,02
-
59,72
156,41
204,79
221,25
226,95
229,23
230,18
230,33
229,75
228,17
224,40
214,10
183,23
105,14
-20,65
-
Etot
0,42
0,18
0,13
0,10
0,09
0,09
0,08
0,08
0,08
0,09
0,10
0,11
0,15
0,26
0,06
-
-
65,
181,
345,
520,
674,
788,
853,
865,
822,
728,
590,
421,
246,
111,
-20,
-
62
September
Time of
the day
8,04
9,00
10,00
11,00
12,00
13,00
14,00
15,00
16,00
17,00
18,00
19,00
20,00
20,51
ωc
-82,79
-68,35
-53,35
-38,35
-23,35
-8,35
6,65
21,65
36,65
51,65
66,65
81,65
96,65
104,25
cos
θz
0,23
0,36
0,46
0,53
0,57
0,57
0,54
0,47
0,37
0,25
0,11
-
Ehor
Mi
trayleigh taerosol tozone tgas
TH2O Edirect B
taa
tas
Ediffuse ra
0,00
319,17
4,28
0,05
0,67
0,99
0,98
0,84
15,52
0,62
0,95
0,70
152,55
0,18
488,10
2,80
0,24
0,78
1,00
0,98
0,85 111,51
0,68
0,97
0,80
200,74
0,13
626,87
2,18
0,39
0,83
1,00
0,98
0,86 235,56
0,73
0,98
0,85
217,59
0,11
726,05
1,88
0,48
0,85
1,00
0,99
0,86 335,49
0,77
0,98
0,87
223,59
0,10
778,87
1,76
0,52
0,86
1,00
0,99
0,86 390,70
0,78
0,99
0,88
225,67
0,10
781,75
1,75
0,52
0,86
1,00
0,99
0,86 393,73
0,79
0,99
0,88
225,77
0,09
734,48
1,86
0,49
0,86
1,00
0,99
0,86 344,23
0,77
0,98
0,87
223,96
0,10
640,28
2,13
0,41
0,84
1,00
0,98
0,86 248,69
0,73
0,98
0,85
218,62
0,11
505,58
2,70
0,26
0,79
1,00
0,98
0,85 125,57
0,68
0,98
0,81
203,67
0,13
339,53
4,03
0,07
0,69
0,99
0,98
0,84
22,36
0,62
0,96
0,72
160,64
0,17
153,44
8,91
0,00
0,25
0,99
0,98
0,81
0,00
0,56
0,83
0,30
67,02
0,38
0,00
0,00
-
Eto
174
320
463
570
628
631
579
477
337
189
72
October
Time of
cos
the day ωc
θz
Ehor
Mi
trayleigh taerosol tozone tgas
TH2O Edirect B
taa
tas
Ediffuse ra
Etot
9,12
64,17
0,00
10,00
0,20 270,72
5,05
0,02
0,60
0,99
0,98
0,83
4,88
0,60
0,94
0,64
130,65
0,21 141,54
63
11,00
12,00
13,00
14,00
15,00
16,00
17,00
18,00
19,00
19,12
50,91
35,91
20,91
-5,91
9,09
24,09
39,09
54,09
69,09
84,09
85,82
0,29 401,86
0,36
0,39
0,39
0,35
0,28
0,17
0,05
-
November
Time of
the day
ωc
9,30
61,28
10,00
50,70
11,00
35,70
492,65
536,89
531,58
477,08
377,09
238,43
70,54
0,00
0,00
cos
θz
Ehor
3,40
0,14
0,74
0,99
0,98
0,84
52,05
0,65
0,97
0,76
2,77
2,55
2,57
2,87
3,63
5,73
19,38
-
0,25
0,30
0,29
0,23
0,11
0,01
0,00
-
0,79
0,80
0,80
0,78
0,72
0,54
-1,12
-
1,00
1,00
1,00
1,00
0,99
0,99
0,98
-
0,98
0,98
0,98
0,98
0,98
0,98
0,97
-
0,85
0,85
0,85
0,85
0,84
0,83
0,79
-
115,11
152,10
147,49
102,94
38,73
1,59
0,00
-
0,68
0,70
0,69
0,67
0,64
0,59
0,53
-
0,97
0,98
0,98
0,97
0,96
0,93
-0,01
-
0,81
0,82
0,82
0,80
0,75
0,59
91,82
-
201,53
0,13
208,25
0,12
207,53
0,12
198,73
0,13
173,79
0,16
114,26
0,24
14,73 -43,00
-
taa
tas
Ediffuse ra
Mi
trayleigh taerosol tozone tgas
-
0,00
-
-
0,05
67,60
20,22
0,00
0,14 192,78
7,09
0,00
-
TH2O Edirect B
-
-
-
-
-
-
-
-1,26
0,98
0,97
0,79
0,00
0,52
-0,13
9,60
0,42
0,99
0,98
0,82
0,13
0,57
0,89
0,47
181,25
-
0,15 240,63
325,12
369,40
364,00
309,95
219,55
121,66
1,53
-
Etot
-
-
12,50
-4,02
6,
89,42
0,29
95,
64
12,00
13,00
14,00
15,00
16,00
16,99
20,70
-5,70
9,30
24,30
39,30
54,21
December
Time of
the day
ωc
10,13
51,24
11,00
38,25
12,00
23,25
13,00
-8,25
14,00
6,75
15,00
21,75
16,00
36,75
16,58
45,51
0,20
0,23
0,23
0,19
0,12
-
279,18
320,94
315,22
262,39
166,06
0,00
cos
θz
Ehor
4,90
4,26
4,34
5,21
8,23
-
Mi
0,02
0,05
0,05
0,02
0,00
-
0,62
0,67
0,66
0,59
0,31
-
0,99
0,99
0,99
0,99
0,99
-
0,98
0,98
0,98
0,98
0,98
-
trayleigh taerosol tozone tgas
-
0,00
-
-
0,06
79,80
17,13
0,00
0,12
0,16
0,16
0,13
0,07
-
170,64
218,85
221,17
177,42
90,60
0,00
8,01
6,25
6,18
7,70
15,09
-
0,00
0,00
0,00
0,00
0,00
-
-
0,83
0,84
0,84
0,83
0,82
-
6,20
16,05
14,35
3,78
0,01
-
0,60
0,62
0,62
0,60
0,56
-
TH2O Edirect B
0,94
0,95
0,95
0,94
0,86
-
taa
0,65
0,70
0,69
0,63
0,37
-
tas
134,73
153,28
150,90
126,54
74,30
-
0,21
0,18
0,19
0,22
0,35
-
Ediffuse ra
-
-
-
-
-
-
-
-
-0,77
0,98
0,97
0,79
0,00
0,53
0,26
-2,93
21,41
0,34
0,50
0,51
0,37
-0,47
-
0,99
0,99
0,99
0,99
0,98
-
0,98
0,98
0,98
0,98
0,97
-
0,82
0,82
0,82
0,82
0,80
-
0,02
0,65
0,73
0,04
0,00
-
0,56
0,58
0,58
0,56
0,53
-
0,86
0,91
0,92
0,87
0,46
-
0,39
0,55
0,55
0,42
-1,03
-
76,91
103,80
105,05
80,78
28,71
-
147,
175,
171,
136,
79,
-
Etot
1,92
-
34,7
0,34 82,4
0,26 110,1
0,26 111,5
0,32 86,3
1,02 36,0
-
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