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Solar Power

The earth receives more energy from the Sun in just one hour than the world’s population uses in a whole year.

The total solar energy flux intercepted by the earth on any particular day is 4.2 X 1018 Watthours or 1.5 X 1022 Joules (or 6.26 X 1020 Joules per hour ). This is equivalent to burning 360 billion tons of oil ( toe ) per day or 15 Billion toe per hour.

In fact the world’s total energy consumption of all forms in the year 2000 was only 4.24 X 1020 Joules. In year 2005 it was 10,537 Mtoe (Source BP Statistical Review of World Energy 2006)


Solar Radiation

Sunlight comes in many colours, combining
low-energy infrared photons (1.1 eV) with high-energy ultraviolet
photons (3.5 eV) and all the visible-light photons between.

The graph below shows the spectrum of the
solar energy impinging on a plane, directly facing the sun, outside the
Earth’s atmosphere at the Earth’s mean distance from the Sun. The area
under the curve represents the total energy in the spectrum. Known as
the “Solar Constant” G0, it is equal to 1367 Watts per square metre (W/m2).

Extraterrestrial Solar Energy Spectrum

The radiant energy falling within the visible
spectrum is about 43% of the total with about 52% in the infra red
region and 5% in the ultra violet region.


The graph below shows the energy at sea level.

Direct energy is the energy received directly from the sun.

Global energy includes energy diffused, scattered or reflected from clouds and energy re-radiated by the earth itself.

Terrestrial Solar Energy Spectrum

Energy received at sea level is about 1kW/m2 at noon near the equator


Irradiance and Insolation

Total solar irradiance is
defined as the the amount of radiant energy emitted by the Sun over all
wavelengths, not just visible light, falling each second on a 1 square
metre perpendicular plane outside Earth’s atmosphere at a given distance
from the Sun. It is roughly constant, fluctuating by only a few parts
per thousand from day to day.

On the outer surface of the Earth’s atmosphere the irradiance is known as the solar constant and is equal to about 1367 Watts per square meter.

The amount of solar energy that actually
passes through the atmosphere and strikes a given area on the Earth over
a specific time varies with latitude and with the seasons as well as
the weather and is known as the insolation (incident solar radiation).

When he Sun is directly overhead the
insolation, that is the incident energy arriving on a surface on the
ground perpendicular to the Sun’s rays, is typically 1000 Watts per
square metre. This is due to the absorption of the Sun’s energy by the
Earth’s atmosphere which dissipates about 25% to 30% of the radiant

Insolation increases with altitude

The terms “irradiance” and “insolation” are often used interchangeably to mean the same thing.


Available Solar Energy

Since the Earth’s cross sectional area is 127,400,000 km², the total Sun’s power it intercepted by the Earth is 1.740×1017 Watts but as it rotates, no energy is received during the night and the
Sun’s energy is distributed across the Earth’s entire surface area so
that the average insolation is only one quarter of the solar constant or
about 342 Watts per square meter. Taking into account the seasonal and
climatic conditions the actual power reaching the ground generally
averages less than 200 Watts per square meter. Thus the average power
intercepted at any time by the earth’s surface is around 127.4 X 106 X 106 X 200 = 25.4 X 1015 Watts or 25,400 TeraWatts.


Integrating this power over the whole year the total solar energy received by the earth will be:

25,400 TW X 24 X 365 = 222,504,000 TeraWatthours (TWh)


To put this into perspective, the total
annual electrical energy (not the total energy) consumed in the world
from all sources in 2004 was 16,600 TWh. Thus the available solar energy
is over 13,000 times the world’s consumption. The solar energy must of
course be converted into electrical energy, but even with a low
conversion efficiency of only 8% the available energy will be 17,800,000
TWh or over a thousand times the consumption. Using the same low
conversion efficiency, the entire world’s electricity demand could be
supplied from a solar panel of 118,000 km2. Theoretically this could be provided by six solar plants of 20,000 km2or
141 km per side, one plant in each of the hot, barren continental
deserts in Australia, China, the Middle East, Northern Africa, South
America and the USA or one large solar plant covering 1% of the Sahara


Unfortunately the Sun’s bounty can only be
harvested during daylight hours and some energy must be stored for use
during the hours of darkness and the requirement to distribute the
energy over great distances to where it is needed make this proposition
impractical. The example merely serves to illustrate the abundance of
the sun’s energy.

What is practical however is to build
smaller, more efficient solar power plants to serve the demands of local
communities using free solar energy when it is available in conjunction
with other other energy sources or some local energy storage where
possible. Despite this, less than 0.1% of the world’s primary energy
demand is supplied by solar energy.


Equivalent Hours of Full Sun (EHS)

of the variation in the intensity of the Sun’s radiation during the day
and also the variations in the length of the day it is difficult to
make comparisons of the Sun’s energy falling upon the Earth at different
locations. The graph opposite shows an example in which the insolation
reaches 1000 W/m2 at noon when the sun is at its highest point in the sky. An insolation of 1000 W/m2 is known as the “Full Sun”. Most of the time the incident energy is
below this value because it depends on the angle of incidence of the
Sun’s rays with the ground, increasing during the day from a very low
value at dawn as the Sun rises to a peak at noon and falling again as
the Sun sets. (See Angle of Incidence below). Similarly the insolation will be reduced as higher latitudes due to the effect of air mass – (See below).

The graph also shows that, in this case, the total received energy over the 10 hours of daylight will be 3.5 kWh.

If the insolation had been constant at 1000 W/m2 the same amount of energy would have been received in 3.5 hours. The
Equivalent Hours of Full Sun is a measure of average insolation at
different locations. In this case the EHS is 3.5 hours.

The available solar energy
and thus the Equivalent Hours of Full Sun (EHS) also depend on the
atmospheric conditions of cloud cover and pollution. See Available Energy – Practical Systems below.


The concept of EHS is
useful for comparing the potential of solar energy systems when
installed at different geographic locations.

Daily Variation in Insolation


Capturing Solar Energy

Solar energy can be captured in two forms, either as heat or as electrical energy.

  • Thermal Systems
  • Thermal systems capture the Sun’s heat energy (infra red radiation) in some form of solar collector and use it to mostly to provide hot water or for space heating, but the
    heat can also used to generate electricity by heating the working fluid
    in heat engine which in turn drives a generator.

  • Photovoltaic Systems
  • Photovoltaic systems capture the sun’s
    higher frequency radiation (visible and ultra violet) in an array of
    semiconductor, photovoltaic cells which convert the radiant energy
    directly into electricity.


The actual solar energy or insolation
reaching a solar collector or array depends on its position on the
Earth, its orientation and it also varies continuously with time as well
as weather conditions.

The amount of energy captured is directly proportional to the area of the Sun’s energy front intercepted by the collector.


Some Geometry

The orientation of the solar collector or the
photovoltaic array with respect to the position of the Sun is a major
determinant in the efficiency of the solar power system.


  • Inclined Planes

Angle of Incidence

The amount of energy
impinging on a collector or array is directly proportional to the area
of the radiation wave-front it intercepts. For optimum energy capture
the collector must be perpendicular to the Sun’s rays when the angle of
incidence is 90°. For a flat plate on the ground this occurs only when
the Sun is directly overhead. Unfortunately unless you live in the
tropics this will never be the case and solar arrays must be tilted
towards the Sun to receive the maximum insolation.


When the incident energy is not perpendicular to the collector, the angle of incidence is (90° – Θ) and the effective area of the collector is A.cosΘ where A is the area of the collector and Θ is the deviation from perpendicular of the radiation.

Incident Energy on an Inclined Plane

Energy Absorption by the Atmosphere


In the diagram above, the Air Mass corresponds to the factor (1/cosΦ)

Air Mass

The Air Mass is a dimensionless
quantity defined as the ratio between the actual path length of the
solar radiation through the atmosphere and the vertical path length
through the atmosphere at sea level.

If the Sun’s radiation is not
perpendicular to the Earth, the transit path through the Earth’s
atmosphere will be longer and hence the energy absorbed on the way to
the collector or array will be greater.

The effect of the longer route through the atmosphere is to increase the energy absorption (or lost energy) by a factor of 1/cosΦ where Φ is the deviation from perpendicular of the radiation, also called the zenith angle.

Thus in the polar regions as Φ approaches 90 degrees (cosΦ>0)
the insolation is very low, even if the collector is pointed directly
at the Sun, due to the longer path through the atmosphere.


  • Altitude
  • Insolation increases with altitude since the
    radiation passes through less air mass hence the energy absorption by
    the atmosphere is less.


Some Astronomy

To calculate how solar insolation varies with
time and with the position of the collector on the Earth’s surface we
need to know a little astronomy.


Though the Earth moves around the Sun, for
the purposes of calculating the energy intercepted by our collectors it
is often convenient to assume that the Earth is stationary and the Sun
moves relative to the earth in much the same way as the ancients did
before Copernicus pointed out their error. Assuming the Earth does not
rotate, the apparent trajectory of the Sun follows a two-dimensional
plane in the sky called the ecliptic.


  • Position
  • The position of the Sun in the sky relative to an observer on Earth is defined by its altitude angle α (solar elevation angle) and its azimuth angle Ψ.


    Azimuth and Altitude of the Sun

  • The Earth’s Orbit
  • The Earth orbits the Sun with one revolution per year in an
    elliptical orbit with the Sun at one of the foci of the ellipse. The
    orbit’s two foci are very close together however so that the orbit is
    almost circular, the distance to the Sun from the perihelion, the point
    in its orbit closest to the Sun, being only about 3% less than its
    distance from the aphelion, its furthest distance.


    Because the orbit is almost circular, the effect of the orbit
    on solar irradiance remains essentially constant throughout the year as
    the Earth orbits the Sun. The actual energy received at any distance
    from the Sun is determined by the inverse square law. Thus a 3% change
    in distance gives rise to a 6% change in the irradiance.


  • The Earth’s Rotation
  • The Earth’s rotation of once per day defines our day and
    night. As the Earth rotates the insolation at any point on its surface
    rises to a maximum at mid day and falls to zero during the night as the
    Earth presents a different face towards the Sun. For maximum efficiency
    the orientation of the collector should follow the Sun as it passes
    overhead from East to West.


  • Latitude
  • A solar collector or array placed on the ground will only
    receive the maximum insolation when the Sun is directly overhead.
    Because the Earth is roughly spherical, the angle between the plane of
    the Earth’s surface and the incident solar radiation will gradually
    increase from 90 degrees as we move away from the equator to the upper
    and lower latitudes by an angle Θ equal to the latitude of the observer. At this point the altitude angle α of the Sun will be (90 – Θ)
    degrees. Because of the increased inclination of the Earth’s surface
    the insolation received by a collector placed on the surface will
    gradually decrease.


    This drawback can be overcome by inclining the collector so
    that it is perpendicular to the Sun’s rays. The amount of elevation from
    the horizontal, the tilt angle, should be equal to the latitude angle Θ of the location of the collector.


    For maximum effect the axis of the inclination should be
    perpendicular to the polar axis. That is, in the Northern hemisphere the
    direction of the collector should point due South.

    Note that the polar axis is not the same as the compass
    bearing because the magnetic poles do not necessarily line up exactly
    with the geometric poles.
    The angle between the magnetic and geographical meridians at any
    place is called the magnetic declination or variation and can be as
    much as 20 degrees or more. It is expressed in degrees east or west to
    indicate the direction of magnetic north from true north.


    Unfortunately the Sun does not appear to follow a constant
    path in the Earth’s equatorial plane. It appears to move North in the
    Summer and South in the Winter. In fact the Sun is stationary and the
    effect is due to the tilt of the Earth’s axis of rotation.


  • The Earth’s Tilt
  • The Earth’s rotational axis is tipped over about 23.45
    degrees from the plane of its orbit. This tilt is essentially constant,
    maintained in that direction due to the gyroscopic action of the earth’s
    rotation, and always points in the same direction relative to the
    stars, so that the North Pole points towards the star Polaris, the North
    Star. Over very long time periods however, measured in thousands of
    years, the direction of Earth’s axis slowly changes due to gyroscopic



    The fixed orientation in space of the Earth’s axis as it
    orbits the Sun determines the length of the day and creates the world’s
    seasons. At the summer solstice, the longest day,. the northern half of
    the Earth is pointing towards the Sun creating summer in the Northern
    hemisphere. The winter solstice, the shortest day in the Northern
    hemisphere occurs when the Earth has travelled 180 degrees around its
    orbit and the Northern hemisphere is pointing away from the Sun.

    From the Earth it appears that the Earth’s rotational axis is
    rocking backwards and forwards. The apparent tilt of the Earth’s axis
    corresponds to the angular position of the Sun at its highest point in
    the sky with respect to an observation point on the plane of the equator
    and is called the solar declination δ (Not to be confused with magnetic variation, also called the declination).

    The vernal (spring) and autumnal equinoxes, in March and
    September when the day and night are the same length, occur when the
    Earth is mid way between the solstices. Then the plane of the tilt is
    perpendicular to the direction of the Sun from the Earth so that the
    insolation is the same on both hemispheres.


    As a result of the Earth’s tilt, the intensity of the
    insolation varies during the year giving rise to the seasons. This is
    not because tilt causes a point on the Earth’s surface to move closer to
    or further from the Sun. The change in distance is negligible. It is
    because of three factors:

    • The Earth’s apparent tilt changes the angle of incidence of
      the solar radiation, changing its insolation per unit area as noted in
      the diagram above.
    • At the same time the tilt also changes the path length of
      the radiation through the atmosphere which in turn changes the amount of
      the Sun’s energy absorbed by the atmosphere. (also shown in the same
      diagram above).
    • The tilt also changes the number of daylight hours.

    These factors all work together to reduce both the intensity and daily duration of the insolation during winter months.


    As seen from the northern hemisphere of the Earth, the
    declination in the elevation of the Sun varies during the course of the
    year between minus 23.45° in the summer and plus 23.45° in the winter.

    Taking into account the solar declination, the altitude angle α of the sun is (90 – Θ ± δ) degrees.

    The inclination angle of solar collectors from the horizontal for maximum efficiency should therefore be (Θ ± δ) degrees and the collector should be able to follow this variation in declination throughout the year.


  • Time
  • Fortunately as a source of renewable energy the Sun is much
    more predictable than the wind. It comes up every morning and goes down
    every night. The intensity of the wind may be extremely variable, but it
    is available 24 hours per day, while solar power is only available
    during daylight hours. At least solar power is reliable and is
    available when it is needed most – during peak demand hours.


    Though the insolation is subject to two temporal variations, a
    diurnal (daily) cycle due to the Earth’s rotation and a yearly cycle
    due to the tilt of the Earth’s axis, we know precisely the magnitude of
    these effects at any time so we can design our solar power systems
    accordingly. What is less predictable however is the affect of the


    Unless they are connected to the grid, systems which must
    provide energy on demand need some form of energy storage or an
    alternative source of energy for the hours of darkness.


Some Meteorology

Unfortunately we have no control over the
weather. Overcast skies can severely reduce the energy received on the
ground. Obviously solar power generating plants are best located in
regions with minimum cloud cover, dust and air pollution. At least we
usually have statistics about regional weather conditions to help in
choosing suitable locations for solar power plants.


For dimensioning a solar power generating
system it is essential to know the number of hours of daylight expected
at the site location. This can normally be obtained from national
meteorological services and environmental research establishments as
well as from NASA in the USA. It helps even more if they are able to
provide tables of expected solar energy for the region.

Note: It is important to check the basis of
the data. Some organisations quote the solar insolation on a horizontal
surface, that is the ground. Others base their data on the insolation of
a collector with a fixed angle of tilt corresponding to the latitude of
the location.


Energy Capture and Collector / Array Orientation

table opposite shows how the effectiveness of a solar array or
collector diminishes as its orientation and tilt move away from the
optimum position.


example shows that to capture maximum solar energy with an array
located at a latitude of 35° North, the optimum array orientation is
pointing due South and the optimum tilt is the same as the latitude, in
this case 35°.

If the array system has to
be mounted on a roof with a pitch of 45° on a building pointing South
West it will only receive a maximum of about 90% of the available solar

Solar Energy Capture

Solar Tracking

As indicated above the amount of energy
captured by a solar system can be maximised if the collector can follow
the ecliptic path of the Sun so that the plane of the collector or array
is always perpendicular to the direction of the Sun.

Automatic mechanical tracking systems make it
possible to track both the azimuth and the elevation of the Sun’s
position to maximise energy capture.


Solar Tracking


Note the lower zenith and the reduced azimuth range of the winter Sun. The chart below shows that, in the UK, the available energy from the winter Sun is
between one sixth and one twelfth of the energy from the summer Sun
depending on the latitude.


  • Azimuth Tracking
  • Azimuth tracking keeps the collector pointing at the Sun as the Earth rotates.

    The insolation varies between zero and its
    maximum value during the course of every day and remains around its
    maximum value for a relatively short period of time. Azimuth tracking
    enables the collector to follow the Sun from East to West throughout the
    day and brings the most benefits.

    Passive systems provide the simplest form
    of azimuth tracking. They have no motors, controllers or gears and they
    don’t use up any of the energy captured by the collector. They depend on
    the differential heating of two interconnected tubes of gaseous
    refrigerants, one on either side of the collector. If the collector is
    not pointing towards the Sun, one side heats up more than the other and
    vaporises its refrigerant. The resulting change in weight is used in a
    mechanical drive mechanism to turn the collector towards the Sun where
    it will remain when the temperature and weight of the two tubes will be

    Active tracking is also possible by
    employing temperature sensors and a control system with linear actuating
    motors taking their drive power from the system.


  • Altitude/Elevation Tracking
  • Elevation tracking enables the collector to
    follow the seasonal variations in the Sun’s altitude but the economic
    benefits are less than for azimuth tracking.

    Compared with the daily variations in
    insolation, the seasonal variations are very slow and the range of the
    variation, due to the solar declination is much more restricted. Because
    of this, reasonable efficiency gains can be obtained simply by manually
    adjusting the elevation of the collectors every two months. To avoid
    the cost and complexity of elevation tracking, it may be more cost
    effective just to specify larger collectors.


  • Dual Axis Tracking
  • Combining azimuth and elevation tracking enables the
    installation to capture the maximum energy using the smallest possible
    collectors but the systems are complex and many installations get by
    with just azimuth tracking.


Solar Collectors

A solar collector is simply a heat
collecting surface which intercepts the Sun’s radiated energy and heats
up a thermal working fluid. In practical thermal systems it is usually
more convenient to focus the Suns heat energy on to a small receiver in
order to obtain a higher temperature rise of the working fluid. Such
collectors are called concentrators.


Typical concentrators are constructed from
parabolic mirrors which reflect the Sun’s parallel rays on to a single
spot at the focus of the mirror.

  • Parabolic Dish
  • A parabolic dish will capture the energy
    intercepted by the dish and concentrate it on a suitable heat absorber
    located at the focus. The amount of energy captured and hence the
    temperature rise of the absorber will be proportional to the area of the
    dish. Size limitations of the dish limit its application to small
    systems of from 10kW to 50kW.

    Parabolic Dish Solar Concentrator
    Parabolic Trough Solar Concentrator
  • Parabolic Trough
  • Larger systems use arrays of parabolic
    trough shaped mirrors oriented north-south to concentrate the solar
    radiation. They usually also include a tracking system to track the
    Sun’s path throughout the day.


    Parabolic Trough Arrays

    Source: US DOE (EERE)

    The thermal absorber, a tube located at
    along the focal line of the mirror, contains the working fluid which is
    heated by the solar radiation to a high temperature and used to drive a
    heat engine.


  • Power Tower
  • An alternative concentrator arrangement
    is the Power Tower which uses a large array of parabolic mirrors focused
    on a solar furnace mounted on the top of a tower. Because of the long
    focal length, the mirrors are almost flat.

    Solar Power Tower


    As with the trough concentrators, the solar furnace is used to raise steam to drive a turbine generator.


    Solar Power Tower

    Source: U.S. NASA

  • Suns – This is a unit
    used by the solar concentrator community to express the degree of
    concentration of the mirror system, similar to the magnification factor
    of a lens. Note that this unit is not precisely defined .


Available Energy – Practical Systems

The table below shows the solar energy
available at two extremes of latitude and provides an indication of the
upper and lower limits of the solar energy falling on the Earth. The
insolation (kWh/m2/day) is the monthly averaged incident
energy falling on a horizontal surface at the given location. Also
called the “Equivalent Sun Hours” or “Hours of Full Sun” (See Definition)


Solar Energy Available at Different Latitudes






Insolation kWh/m2/Day



Anchorage, Alaska






2 Axis










2 Axis



    Source NREL


Because of cloud cover and pollution, the
quoted hours of “full Sun” are substantially less than the actual hours
of daylight. In sunnier climes, an average of 33% of solar irradiation
comes from diffuse light but for the majority of locations this is
typically more than 50%. The equivalent hours of full Sun takes into
account the affect of overcast or partially cloudy skies.


System Dimensioning – Energy Capture

Much care is needed in specifying solar array
sizes to meet system power requirements. Using yearly average
insolation figures for the chosen location may be acceptable if all that
is required is a grid connected system with an average annual
generating capacity, but this is almost never the case and it certainly
does not apply to stand alone systems.

Averages can be very misleading, even within the month.

The following table gives the monthly average, and yearly average, insolation at two locations in the UK.


Daily Insolation Levels (kWh/m2/day) at Locations in the UK


















55′ 55″ N

3″ 10″ W















51′ 32″ N

0′ 5″ W














Monthly Averaged Insolation Incident On A Horizontal Surface (kWh/m2/day)

Source NASA


If the system capacity were to be based on
the yearly average, for most practical installations there would be a
surplus of energy in the summer and a shortfall in winter. A stand alone
system would have to be dimensioned to be able to provide the peak load
during the winter months, otherwise an auxiliary source of power must
be provided. The system would then be over-specified for the summer
months and some form of reducing the capacity or dumping the excess
energy must be found. A hybrid system combining wind and solar power could be the answer.


Energy Storage

Because no power is provided during the hours
of darkness, the stand alone systems must generate and store sufficient
energy during the day to satisfy the peak daily load. The storage
should also be sufficient to cover several days when no sunlight is
available. Batteries are normally used as a buffer to provide the
necessary storage to guarantee short term continuity of supply by
storing surplus energy during the day for use during the night and
during periods of overcast skies. Unfortunately it is not practical to
store the summer’s surplus energy for use during the winter.


Solar Power Generation (Thermal)

Electricity generation in a solar thermal
plant occurs in two stages. First the heat energy from the Sun is
captured and used to heat a working fluid which is then used in a second
energy transformation stage to generate the electricity. Note that the
thermal energy comes from the Sun’s radiation and not from the air whose
temperature will usually be much lower than the temperature of the
working fluid. The actual operating temperature reached by the working
fluid will depend on the rate at which the thermal energy is being
extracted by the working fluid (the flow rate) and delivered to the
electricity generating system.

A solar thermal power plant usually has a
system of mirrors to concentrate the sunlight on to an absorber, the
absorbed energy then being used to power a heat engine which in turn
drives a rotary generator. In large scale systems, the heat engine is
usually a turbine driven by steam or other vaporous working fluid. In
small scale systems the heat engine may be a Stirling engine.


Electricity Generating Systems

Large Scale Thermal Plants

The system below is designed to capture the thermal energy radiated from the sun.


Solar Thermal Power Plant


Thermal energy from the Sun is intercepted by
a concentrator which focuses the energy on a heat absorber containing
the working fluid, usually a synthetic oil, which is heated by the solar
radiation to a high temperature typically 400° C. The system may use a binary cycle in which the heated oil is passed through a heat exchanger to raise
steam which is used to drive a conventional turbine and generator in a
separate circuit.

To maintain the thermal efficiency of the
turbine, the working fluid leaving the heat exchanger should not be
allowed to cool down. Solar plants are therefore supplemented by
gas-fired boilers which generate about a quarter of the overall power
output and maintain the temperature overnight.

Several such installations in modules of 80
MW are now operating and solar conversion efficiencies of between 15%
and 23% have been achieved. Each module requires about 50 hectares of
land and needs very precise engineering and control. Power costs are two
to three times that of conventional sources.


Small Scale Thermal Plants

Steam turbines are only practical for very large installations. Stirling Engines are often used in small systems to drive the electrical generator.


Solar Stirling

Domestic thermal generating
plants typically use an array of water filled panels or a small array of
parabolic trough concentrators to capture the Sun’s thermal energy.
Very small system such as those used in space applications may simply
use a parabolic dish to capture the energy.


Small Scale Solar Thermal Power


The working fluid is then used as the
external heat source for powering the Stirling engine which in turn
drives a rotary generator.

An off-grid stand alone solar electric system must have batteries supported by Balance-of-System (BOS) components including chargers, inverters and controllers to manage the
energy flows in order to provide power on demand. This makes the system
very expensive. Grid connected systems also need power conditioners and
control systems if surplus energy is to be sold back to the utility

Efficiencies achieved with small scale systems range from 18% to 23%.


Domestic Water Heating Applications – A brief diversion

Many small domestic solar thermal systems are merely used for water heating and not for generating electricity.


  • Practical Systems
  • The working fluid is water, circulating
    through a rooftop mounted solar panel and fed directly into the
    domestic hot water system. As an alternative, the working fluid may be
    passed through a heat exchanger consisting of a coiled pipe in the hot
    water storage tank to heat the water indirectly.

    The front surface of the solar panel is
    double glazed, allowing the Sun’s radiation to pass through to heat up
    the water flowing through the panel while preventing heat loss from the
    warmer water due to convection and conduction in the opposite direction
    (from the panel to the colder atmosphere). The rear surface of the panel
    is also insulated to prevent heat loss in that direction.

    The system works in cold weather because
    the water is heated by the Sun’s radiation, not by the ambient air from
    which it is insulated.


    • Water Temperature
    • An elegant, self regulating solution for
      maintaining the water temperature is provided by incorporating a small,
      subsidiary photovoltaic panel (see below) to generate the electrical energy needed to power the water circulation pumps instead of using mains electricity.

      At sunrise, the pump remains switched off
      until the water reaches its operating temperature at which point the
      pump is switched on. As the Sun’s radiation increases during the
      morning, the water temperature will rise, but at the same time the solar
      powered pump will run faster, increasing the water flow and thus
      transfering heat more quickly from the panel to the hot water storage
      tank. By suitably dimensioning the pump and the photovoltaic panel, the
      heat transfer rate from the panel can be matched to the heat absorption
      rate from the Sun thus maintaining a constant water temperature. As the
      received Sun’s energy wanes in the afternoon the process is reversed,
      the pump runs more slowly reducing the rate at which heat is extracted
      from the panel thus maintaining its temperature. Being completely
      independent of the electricity grid, these systems have the added
      economic and environmental benefits that no electrical energy is drawn
      from the grid for running the pumps.

    • Temperature Limits
    • With water as the working fluid, the system
      is prone to freezing and boiling unless special precautions are taken.
      Low cost systems allow the water to freeze in very cold and dark
      environments by using flexible freeze-tolerant, silicone rubber
      pipework which is sufficient to accommodate the expansion of the water
      as it turns to ice. The volume of water used in solar thermal panels is
      very small, typically around 2 or 3 litres and is spread over a very
      large area to capture the maximum solar radiation. The high received
      radiation acting on a low water volume enables the water to heat up very
      quickly but for the same reason makes it susceptible to boiling. Unless
      there is a constant water flow to a storage tank with the heated water
      in the panel being replaced by cold water from the tank, the water could
      reach temperatures of 150 degrees C or more and for this reason the
      water pumps must be continually switched on. Even so, the possibility of
      boiling still remains, even with the pumps running, if the system is
      incorrectly dimensioned. The equilibrium temperature reached will depend
      on the balance between the solar energy captured by the panel and the
      thermal energy absorbed in the storage tank, the rate at which it is
      withdrawn from the tank and the system heat losses. Using a very small
      panel coupled to a very large tank with high hot water usage will result
      in a low water temperature in the tank. Conversely using a very large
      panel with a very small tank could result in boiling, particulaly if
      the hot water usage is very low. This need not be a disaster since the
      water content in the panel is very low and system could be designed to
      allow the steam to vent in case of boiling.

    • Efficiency
    • Energy conversion efficiencies achieved in
      these pure thermal applications may be three or four times the
      efficiency of photovoltaic applications though their applications are
      much more limited.

    • Economics
    • In higher latitudes the available solar
      energy captured by practical domestic installations may be sufficient to
      provide hot water for washing and showering but not enough to supply
      building space heating requirements during the colder months. Back-up
      heating systems will consequently be needed to cater for the base load
      to satisfy these requirements. Because the supply of solar energy is
      intermittent, the conventional heating system must fill in the gaps and
      there is little opportunity to downsize it. The householder will
      therefore, most likely have to pay the capital costs of a base load
      system capable of supplying the full heating load as well as the solar
      heating system even though the conventional heating system will not be
      working at full capacity most of the time.

      Domestic solar thermal systems may not
      generate electricity directly but they do contribute to a reduction in
      the use of electrical energy and its associated costs.

      • Example
      • Useful Energy Captured

        The table above shows that in the UK, the average solar radiation received is about 2.5 kWh / M2 / day. A single solar panel with an area of 3 M2 will therefore capture 2.5 x 3 x 365 = 2737 kWh of energy per year.
        With a system conversion efficiency of around 40% and less than optimal
        orientation of a typical rooftop mounted solar panel, the maximum usable
        energy received by a single panel system will be around 1000 kWh. This
        is roughly equivalent to the energy supplied by a 3 kW immersion heater
        used for one hour per day. As always however, averages can be
        misleading. In the summer, the solar panel could deliver an “average
        of about 5 kWh of heating energy per day, but in the winter this could
        be as low as 0.4 kWh per day. The energy captured can of course always
        be increased by increasing the number of solar panels employed in the

        Cost Savings

        The cost saving will depend on whether the
        solar system is replacing 1000 kWh of heating energy supplied by a gas
        or an electric water heating system and the associated tarriff charged
        for the energy. With UK domestic gas currently costing less than £0.03
        per kWh ($0. 045) and electricity costing about £0.10 per kWh ($0.15)
        the annual savings are likely to be somehwere between £30 and £100 ($50
        to $150).

        Since typical single panel installations
        cost around £2,500 or £3,000 ($4,000 to $5,000), unless the systems
        qualify for a government subsidy or there is a very large increase in
        energy costs, the payback time for the investment will be measured in
        decades rather than years. Saving the planet can be quite expensive.

        Carbon Footprints

        As with wind power, if the investment fails the conventional economic tests, the notion of carbon footprints is often used to jusify the expense, based on the potential for
        reducing the amount of greenhouse gases emitted by alternative methods
        of power generation.


        See also Domestic Solar PV System Economics below.


Solar Power Generation (Voltaic)

Solar voltaic power generation is the direct conversion of solar energy into electricity.

Sunlight comes in many colours, combining low-energy (1.1 electronVolts (eV)) infrared photons with high-energy (3.5 eV) ultraviolet photons and all the rainbow of
visible-light photons in between. Solar cells, also called photovoltaic
or PV cells, are semiconductor devices designed to capture these photons
and convert their energy directly into electrical energy.


How Solar Cells Work

When a photon with sufficient energy impinges
upon a semiconductor it can transfer enough energy to a electron to
free it from the bonds of the semiconductor’s valence band so that it is
free to move and thus carry an electric current. The junction in a
semiconductor diode provides the necessary electric field to cause the
current to flow in an external circuit.

A more detailed explanation of how solar cells work is given in the section on photovoltaic diodes.


The typical output voltage of a PV cell is
between 0.5 and 0.6 Volts and the energy conversion efficiency ranges
from less than 10% to over 20%. An array of cells can therefore
generate about 200 Watts of electrical power per square metre when
illuminated by solar radiation of 1000 Watts per square metre. The
corresponding current density will be about 400 Amps/m2. Because of climatic conditions the intensity of the insolation rarely reaches 1000 W/m2.

Practical cells are also much smaller than
one square meter with actual sizes of commercially available cells
ranging from about one centimetre square to 15 centimetres square. The
corresponding output Wattages for these cells range from 20 milliWatts
to about 4 Watts.


PV Cell and Module Ratings

  • Standard Test Conditions (STC)
  • In order to compare solar cells on a like
    for like basis a set of Standard Test Conditions (STC) has been defined.
    The conditions are: normal irradiance of 1000w/m2 , cell temperature 25 °C and Air Mass =1.5

  • Air Mass
  • The receiving surface corresponding to AM 1.5 is defined as
    an inclined plane at 37° tilt (the average latitude in the USA) toward
    the equator, facing the sun. In this case, the surface normal points to
    the sun, at an elevation of 48.81°, its zenith angle, above the horizon.

  • Rated Power
  • Rated Power is defined as the maximum power (Wp or kWp) generated by the cell or module under the Standard Test Conditions.


Solar Cell Operating Characteristics

The graph below shows that with constant
irradiance the output voltage of a cell or an array of cells falls as it
is called upon to deliver more current.

Photovoltaic Array Voltage/Current Characteristic


Maximum power delivery occurs the voltage has dropped to about 80% of open circuit voltage voltage.

The Fill Factor (FF) is defined as the ratio
between the power at the maximum power point and the product of the open
circuit voltage and short circuit current. It is typically better than
75% for good quality solar cells.


Photovoltaic Array Irradiance Characteristic

The short
circuit (SC) current is directly related to the number of photons
absorbed by the semiconducting material and is thus proportional to
light intensity.

The conversion efficiency
is therefore reasonably constant so that the power output is
proportional to the irradiance down to fairly low levels, however the
efficiency is reduced if the cell temperature is allowed to rise.

The open circuit (OC) voltage varies only slightly with light intensity.

As temperature increases, the band gap of the intrinsic semiconductor shrinks, and the open circuit voltage (Voc) decreases.

At the same time, the lower
band gap allows more incident energy to be absorbed because a greater
percentage of the incident light has enough energy to raise charge
carriers from the valence band to the conduction band. A larger
photocurrent results.

The increase in the current
for a given temperature rise however is proportionately lower than the
decrease in voltage. Hence the efficiency of the cell is reduced.

Photovoltaic Array Temperature Characteristic


Solar Cell Efficiency

The following graphs show the same information as those above
but in a slightly different form showing how increased temperature
reduces the efficiency.


PV Array EfficiencyPV Array Power


In real outdoor conditions the rated peak
power Wp is seldom achieved, since module temperature usually is more in
the range of 40°C – 60°C. Efficiency can be improved by cooling the
cells and some systems have been designed to make use of the heat
absorbed by the cooling fluid in solar heating applications.


Solar Cell Types

Several types of solar cells have been developed with the aims of reducing costs and improving efficiencies.

  • Crystalline Silicon Solar Cells
  • Benefiting from the manufacturing experience of the
    semiconductor industry, crystalline silicon is the leading solar cell
    material, though still relatively expensive. Monocrystalline cells are
    cut from single crystals of high purity electronics grade silicon.
    These cells are about 25 percent efficient at best. Using the easier to
    manufacture polycrystalline silicon cut from from a block of crystals
    or less pure, so called “solar grade” silicon, efficiencies may be only
    about 15% or 16% due to the effect of grain boundaries or impurities but
    they cost a fraction of single crystal electronics grade cells.

  • Amorphous Silicon Solar Cells
  • Amorphous Silicon has been employed for many years in the
    manufacture the solar cells used for powering electronic calculators and
    watches and promises the possibility of low cost, higher power cells.
    Amorphous material appears like a solid but has no regular crystal
    lattice structure. Glass is an example of such materials. The presence
    of controlled quantities of certain “impurity” elements such as hydrogen
    and the random crystal lattice formation actually enhance the otherwise
    very low conversion efficiency. Typical cell efficiencies range from 5%
    to 10%.

    Manufacturing yield is still a problem and the cells suffer from degradation when exposed to the sun.

  • Thin Film Silicon Solar Cells
  • Thin film cells are made by depositing the active photovoltaic
    material, such as amorphous silicon or other semiconductor onto a glass
    or other substrate together with the necessary current collecting
    contacts. The cell construction is much less costly than using
    semiconductor wafers and the manufacturing process is also simpler as
    well as being suitable for making cells with a much larger area and
    hence current carrying capability. Efficiencies of 11% to 14% have been
    achieved with this construction.

    PV systems on flexible polymer substrates have also been made
    using Copper Indium Gallium Selenide (CIGS) active material with
    efficiencies of 10%.

  • Multi Layer (Tandem) Solar Cells
  • Better conversion efficiencies are possible by using multiple
    layers of differing semiconductor materials, optimised for different
    wavelengths, in a single device. This can raise the theoretical
    efficiency limit, currently about 30% for a single junction device, to
    about 45% for a three junction cell.

    Efficiencies of over 33% have already been achieved in practical devices.

  • Exotic Materials
  • Materials such as Gallium Arsenide, Copper Indium Diselenide,
    Cadmium Telluride and Indium Nitride have been employed to provide
    particular characteristics to optimise solar cells for specific

    Gallium Arsenide is used for military and aerospace
    applications in a variety of cells in combination with other elements
    because of it’s suitability for capturing high energy photons (ultra
    violet radiation), high potential conversion efficiency and its ability
    to withstand high temperatures. It is however more difficult to
    manufacture and cells using Gallium Arsenide can be 100 times more
    expensive than commercial silicon based cells.

    Copper Indium Diselenide and Cadmium Telluride are used in
    polycrystalline form in low cost thin film cells because of their ease
    of manufacture and reasonable yields. Efficiencies are however low
    ranging from 8% to 14%

    Indium Nitride is suitable for capturing low energy photons
    (infra red radiation) making it suitable for full spectrum devices when
    used in tandem solar cells in combination with other materials such as
    Gallium Arsenide which capture the high energy photons.

  • Electrochemical Solar Cells – Dye Sensitised Solar Cells (DSSC or Grätzel Cells)
  • Relatively new, these cells are low cost devices which use dye
    sensitised Titanium dioxide in combination with a liquid electrolyte
    to generate the current. Up to now they are only available in small
    sizes with efficiencies between 7% and 10%.


Solar PV Collectors

Solar cells are usually sold in modules built
up from a number of cells arranged in series and / or parallel to
provide convenient or commonly used voltages and power ratings.

Solar Arrays

Modules can be similarly interconnected to create larger arrays with the desired peak DC voltage and current.



As with thermal collectors, concentration of
the incident energy on to a smaller surface is possible. For very small
applications, optical mirrors and lenses are used.


Maximum Power Point Tracking (MPPT)

A power source will deliver its maximum power
to a load when the load has the same impedance as the internal
impedance of the power source. (Jacobi’s Law). Unfortunately, batteries are far from the ideal load for a solar array and the mismatch results in major efficiency losses.

A typical PV array designed to charge 12 Volt
batteries delivers its maximum power at an operating voltage around 17
Volts. Lead Acid batteries are normally charged up to 14 Volts though
the voltage quickly drops to 12 Volts as they start to deliver current
and lower still as the depth of discharge (DOD) increases.
In its simplest form, charging is carried out by connecting the PV array
directly across the battery. The battery however is a power source
itself and presents an opposing voltage to the PV array. This pulls the
operating voltage of the array down to the voltage of the discharged
battery and this is far from the optimum operating point of the array.

The diagram below shows the performance of a17
Volt, 4.4 Amp, 75 Watt PV array used to top up a 12 Volt battery. If
the actual battery voltage is 12 Volts, the resulting current will only
be about 2.5 Amps and the power delivered by the array will be just over
50 Watts rather than the specified 75 Watts: an efficiency loss of over
Maximum Power Point Tracking is designed to overcome this problem.


Maximum Power Point Tracking (MPPT)


The power tracker module is a form of voltage regulator
which is placed between the PV array and the battery. It presents an
ideal load to the PV array allowing it to operate at its optimum
voltage, in this case 17 Volts, delivering its full 75 Watts regardless
of the battery voltage. A variable DC/DC converter in the module
automatically adjusts the DC output from the module to match the battery
voltage of 12 Volts.
As the voltage is stepped down in the DC/DC converter, the
current will be stepped up in the same ratio. Thus the charging current
will be 17/12 X 4.4 = 6.2 Amps and, assuming no losses in the module,
the power delivered to the battery will be 12 X 6.23 = the full 75 Watts
generated by the PV array.
In practice the converter losses could be as high as 10%.
Nevertheless a substantial efficiency improvement is possible.


It is not enough however to match the
voltage at the specified maximum power point (MPP) of the PV array to
the varying battery voltage as the battery charges up. Due to changes in
the intensity of the radiation falling on the array during the day as
well as to changes in the ambient temperature, the operating
characteristic of the PV array is constantly changing and with it the
MPP of the PV also changes. Thus we have a moving reference point and a
moving target. For optimum power transfer, the system needs to track the
MPP as the solar intensity and ambient temperature changes in order to
provide a dynamic reference point to the voltage regulator.

High performance MPPT modules may
incorporate software algorithms to take account of the variations in
insolation and temperature. A typical job for fuzzy logic or a neural network. Alternatively the optimisation can be accomplished in hardware by means of a perturbation signal incorporated in a feedback loop which drives the system operating point to the MPP.

A small dither voltage is
superimposed on the PV voltage and its affect on the regulator output
current feeding the battery is monitored. If the current drawn by the
battery increases when the dither voltage increases, then the operating
point has moved towards the MPP and therefore, the operating voltage
must be increased in the same direction. On the other hand, if the
current into the battery decreases, then the operating point has moved
away from the MPP and the the operating voltage must be decreased to
bring it back.


Large Scale Photovoltaic Plants

Several large scale grid connected PV power plants have been
constructed throughout the world, mostly of 300 kW to 500 kW capacity
but some as high as 10MW. Up to now deployment of large scale plants has
been limited to experimental installations by the high cost of the
solar panels. With typical efficiencies of 10% or less, a 500 kW plant
will need over 5000 square metres of PV panels costing $1.0 per Watt as
well as large scale inverters capable of handling the full system power


Small Scale Photovoltaic Plants and Domestic Applications

The diagram below shows the basic building blocks of a small
stand-alone off-grid PV power generating system. A grid connected
system would not need the battery and MPPT power tracking system. They
do however need alternative capacity to come on stream to carry the load
during the hours of darkness.


Photovoltaic Electric Power Genertaion


Photovoltaic System Dimensioning


  • Array sizes for Photovoltaic System
  • The following example show the array sizes necessary to
    generate 10 kWh of usable energy with an average daily insolation of 2
    kWh/m2/day. Note that the results are heavily dependent on the efficiency assumptions used.

    Needless to say the array must not be shaded by objects such as trees or buildings.


    • Example
    • Energy received per unit area = Insolation X Solar conversion efficiency.


      The area required for a given energy capture = Energy required ÷ ( Insolation at the desired location X Solar conversion efficiency)

      Using an efficient (expensive) photovoltaic array with a conversion efficiency of 15% the area of the array will be:

      10÷(2 X 0.15) = 33.3 m2

      Insolation data is usually provided for the energy falling
      on a flat surface. By tilting the array to an angle corresponding to the
      latitude of the location, an extra 10% of energy can be captured
      reducing the area required to 30 m2. See the diagram showing Array Orientation

      This advantage will be lost however if the array is to be mounted on a roof which is not optimally aligned towards the Sun.

      If the array is free standing on the ground, and not
      constrained to be used on a roof, a solar tracking system can be used
      to enable more of the Sun’s energy to be captured. A 30% improvement is
      possible reducing the required array area to about 21 m2


      Note that the PV array output is DC electrical power.

      To provide AC power there would be further electrical losses
      of 10% to 20% in the voltage regulator, inverter and control circuits.


      • Grid-connected Systems
      • Assuming 20 % electrical system losses, a fixed PV array with an area of around 36 m2, or a solar tracking PV array of 25 m2 would be required to provide 10 kWh of AC power per day.


      • Stand Alone Systems
      • Off-grid systems are subject to the same performance
        parameters as grid-connected systems however since they also use battery
        storage they suffer from an extra efficiency loss of up to 30% due to
        the back emf of the battery.

        Unless an MPPT tracking system is used to reduce these losses the array would have to be 30%
        bigger to compensate. Thus to provide the same 10 kWh of AC power per
        day in a stand-alone system, the required PV array area would have to be
        47 m2 for a fixed installation and 33 m2 for a solar tracking system.


      Electricity consumption in many households in Europe and the
      USA is 2 or 3 times more than 10 kWh per day, particularly for those
      willing to invest in solar PV electricity generation. (See Energy Demand Table). This implies that very large PV arrays with areas up to 150 m2 or more, probably larger than the available South facing roof surface, would be needed to satisfy their energy demands.


      All of the above is based on an average insolation of 2 kWh/m2/day,
      but in northern temperate zones the winter insolation is likely to be
      less than a quarter of the average for the location. See the table for Energy Availability and Energy Capture above. Thus the available energy will be only 2.5 kWh/day during the
      winter months or the systems would need to be four times bigger in order
      to supply the same 10 kWh/day of electrical energy in the winter.


    Domestic Solar PV System Economics


    • Costs
    • According to the UK Government Energy Saving Trust, the
      costs for installing a solar PV system vary greatly. An average
      domestic system is quite small generating around 2.2 kWp and costs
      around �12,000 ($18,000). Larger solar electricity systems can cost in
      the region of �4,500 ($7,000) to �8,000 ($12,000) per kWp, reducing
      slightly as the system size increases.

    • Benefits
    • A 2.2 kWp system only delivers the full 2.2 kW of power under Standard Test Conditions of 1000 W/m2 insolation. It would generate 52.8 kWH (52.8 Units) of electricity per
      day if the Sun was directly overhead and shining constantly day and
      night. But the table above shows that the average insolation in the UK is only about 2.5 kWh/m2/day. This is equivalent to 2.5 hours of full Sun (see EHS above) per day, not 24 hours. Thus the actual electrical energy output
      from the PV system in the UK will be about 5.5 kWh per day or 2,000 kWh
      per year.

    • Payback
    • Buying 2,000 kWh of electrical energy from the local utility
      company would cost £200 ($300) with the curent costs of electricity at
      £0.10 ($0.15) per unit. Ignoring maintenance costs, this gives a payback
      period of sixty years.

      Fortunately, many governments provide generous grants to
      subsidise the installation and/or operation of solar power systems thus
      reducing the capital outlay and decreasing the investment payback time.

    •  Selling surplus energy back to the utility company
    • The average UK household consumes about 5,000 kWh of
      electrical energy per year or around 14 units per day. The likelihood of
      a domestic installation as described above having regular surpluses is
      quite remote.

      Furthermore, feeding electrical energy back into the grid
      involves the obligatory installation of additional, costly metering and
      safety systems as well as synchronisation electronics so that this
      option is only economically justifiable for installations with
      relatively large surplusses.


    Beware when the solar panel salesman comes knocking!


    See also Domestic Solar Heating and a comparison of Electricity Generating Costs for different fuels.


  • Balance of System (BOS) Components
  • The associated BOS components needed to complete the system are described in the section on Small Scale Systems.


  • Other PV System Considerations
  • Converting the direct current output of the
    PV array to alternating current is both costly and inefficient. Some of
    this cost and waste can be avoided by using household appliances
    designed to run on DC power where they are available.

    Similarly it is not sensible to run heaters from PV systems.


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